{ "cells": [ { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from IPython.display import YouTubeVideo\n", "from scipy.stats import norm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Multidimensional Kalman Filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## for a Constant Acceleration Model (CA)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Situation covered: You have a Position Sensor (e.g. a Vision System) and try to calculate velocity ($\\dot x$ and $\\dot y$) as well as position ($x$ and $y$) of a ball in 3D space." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/jpeg": 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\n", "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "YouTubeVideo(\"tIIJME8-au8\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## State Vector - Constant Acceleration" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Constant Acceleration Model for Motion in 3D\n", "\n", "$$x= \\left[ \\matrix{ x \\\\ y \\\\ z \\\\ \\dot x \\\\ \\dot y \\\\ \\dot z \\\\ \\ddot x \\\\ \\ddot y \\\\ \\ddot z} \\right]$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Formal Definition:\n", "\n", "$$x_{k+1} = A \\cdot x_{k} + B \\cdot u_k$$\n", "\n", "Hence, we have no control input $u$.\n", "\n", "$$x_{k+1} = \\begin{bmatrix}1 & 0 & 0 & \\Delta t & 0 & 0 & \\frac{1}{2}\\Delta t^2 & 0 & 0 \\\\ 0 & 1 & 0 & 0 & \\Delta t & 0 & 0 & \\frac{1}{2}\\Delta t^2 & 0 \\\\ 0 & 0 & 1 & 0 & 0 & \\Delta t & 0 & 0 & \\frac{1}{2}\\Delta t^2 \\\\ 0 & 0 & 0 & 1 & 0 & 0 & \\Delta t & 0 & 0 \\\\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & \\Delta t & 0 \\\\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & \\Delta t \\\\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\end{bmatrix} \\cdot \\begin{bmatrix} x \\\\ y \\\\ z \\\\ \\dot x \\\\ \\dot y \\\\ \\dot z \\\\ \\ddot x \\\\ \\ddot y \\\\ \\ddot z\\end{bmatrix}_{k}$$\n", "\n", "$$y = H \\cdot x$$\n", "\n", "Position ($x$ & $y$ & $z$) is measured with vision system:\n", "\n", "$$y = \\begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\end{bmatrix} \\cdot x$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Initial Uncertainty" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "P = 100.0*np.eye(9)\n", "\n", "fig = plt.figure(figsize=(6, 6))\n", "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n", "plt.title('Initial Covariance Matrix $P$')\n", "ylocs, ylabels = plt.yticks()\n", "# set the locations of the yticks\n", "plt.yticks(np.arange(10))\n", "# set the locations and labels of the yticks\n", "plt.yticks(np.arange(9),('$x$', '$y$', '$z$', '$\\dot x$', '$\\dot y$', '$\\dot z$', '$\\ddot x$', '$\\ddot y$', '$\\ddot z$'), fontsize=22)\n", "\n", "xlocs, xlabels = plt.xticks()\n", "# set the locations of the yticks\n", "plt.xticks(np.arange(7))\n", "# set the locations and labels of the yticks\n", "plt.xticks(np.arange(9),('$x$', '$y$', '$z$', '$\\dot x$', '$\\dot y$', '$\\dot z$', '$\\ddot x$', '$\\ddot y$', '$\\ddot z$'), fontsize=22)\n", "\n", "plt.xlim([-0.5,8.5])\n", "plt.ylim([8.5, -0.5])\n", "\n", "from mpl_toolkits.axes_grid1 import make_axes_locatable\n", "divider = make_axes_locatable(plt.gca())\n", "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n", "plt.colorbar(im, cax=cax)\n", "\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Dynamic Matrix" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(9, 9)\n" ] } ], "source": [ "dt = 0.01 # Time Step between Filter Steps\n", "\n", "A = np.matrix([[1.0, 0.0, 0.0, dt, 0.0, 0.0, 1/2.0*dt**2, 0.0, 0.0],\n", " [0.0, 1.0, 0.0, 0.0, dt, 0.0, 0.0, 1/2.0*dt**2, 0.0],\n", " [0.0, 0.0, 1.0, 0.0, 0.0, dt, 0.0, 0.0, 1/2.0*dt**2],\n", " [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, dt, 0.0, 0.0],\n", " [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, dt, 0.0],\n", " [0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, dt],\n", " [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0],\n", " [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0],\n", " [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])\n", "print(A.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Measurement Matrix" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here you can determine, which of the states is covered by a measurement. In this example, the position ($x$ and $y$) is measured." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1. 0. 0. 0. 0. 0. 0. 0. 0.]\n", " [0. 1. 0. 0. 0. 0. 0. 0. 0.]\n", " [0. 0. 1. 0. 0. 0. 0. 0. 0.]] (3, 9)\n" ] } ], "source": [ "H = np.matrix([[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n", " [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n", " [0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]])\n", "print(H, H.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Measurement Noise Covariance Matrix $R$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1. 0. 0.]\n", " [0. 1. 0.]\n", " [0. 0. 1.]] (3, 3)\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rp = 1.0**2 # Noise of Position Measurement\n", "R = np.matrix([[rp, 0.0, 0.0],\n", " [0.0, rp, 0.0],\n", " [0.0, 0.0, rp]])\n", "print(R, R.shape)\n", "\n", "fig = plt.figure(figsize=(4, 4))\n", "im = plt.imshow(R, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n", "plt.title('Measurement Noise Covariance Matrix $R$')\n", "ylocs, ylabels = plt.yticks()\n", "# set the locations of the yticks\n", "plt.yticks(np.arange(4))\n", "# set the locations and labels of the yticks\n", "plt.yticks(np.arange(3),('$x$', '$y$', '$z$'), fontsize=22)\n", "\n", "xlocs, xlabels = plt.xticks()\n", "# set the locations of the yticks\n", "plt.xticks(np.arange(4))\n", "# set the locations and labels of the yticks\n", "plt.xticks(np.arange(3),('$x$', '$y$', '$z$'), fontsize=22)\n", "\n", "plt.xlim([-0.5,2.5])\n", "plt.ylim([2.5, -0.5])\n", "\n", "from mpl_toolkits.axes_grid1 import make_axes_locatable\n", "divider = make_axes_locatable(plt.gca())\n", "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n", "plt.colorbar(im, cax=cax)\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Process Noise Covariance Matrix $Q$ for CA Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Position of an object can be influenced by a force (e.g. wind), which leads to an acceleration disturbance (noise). This process noise has to be modeled with the process noise covariance matrix Q.\n", "\n", "To easily calcualte Q, one can ask the question: How the noise effects my state vector? For example, how the jerk change the position over one timestep dt. With $\\sigma_{j}$ as the magnitude of the standard deviation of the jerk, which distrubs the ball in 3D space. We do not assume cross correlation, which means if a jerk will act in x direction of the movement, it will not push in y or z direction.\n", "\n", "We can construct the values with the help of a matrix $G$, which is an \"actor\" to the state vector." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Symbolic Calculation" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "from sympy import Symbol, Matrix\n", "from sympy.interactive import printing\n", "printing.init_printing()\n", "dts = Symbol('\\Delta t')" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\left[\\begin{matrix}\\frac{\\Delta t^{3}}{6}\\\\\\frac{\\Delta t^{2}}{2}\\\\\\Delta t\\end{matrix}\\right]$$" ], "text/plain": [ "⎡ 3⎤\n", "⎢\\Delta t ⎥\n", "⎢─────────⎥\n", "⎢ 6 ⎥\n", "⎢ ⎥\n", "⎢ 2⎥\n", "⎢\\Delta t ⎥\n", "⎢─────────⎥\n", "⎢ 2 ⎥\n", "⎢ ⎥\n", "⎣\\Delta t ⎦" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Gs = Matrix([dts**3/6, dts**2/2, dts])\n", "Gs" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\left[\\begin{matrix}\\frac{\\Delta t^{6}}{36} & \\frac{\\Delta t^{5}}{12} & \\frac{\\Delta t^{4}}{6}\\\\\\frac{\\Delta t^{5}}{12} & \\frac{\\Delta t^{4}}{4} & \\frac{\\Delta t^{3}}{2}\\\\\\frac{\\Delta t^{4}}{6} & \\frac{\\Delta t^{3}}{2} & \\Delta t^{2}\\end{matrix}\\right]$$" ], "text/plain": [ "⎡ 6 5 4⎤\n", "⎢\\Delta t \\Delta t \\Delta t ⎥\n", "⎢───────── ───────── ─────────⎥\n", "⎢ 36 12 6 ⎥\n", "⎢ ⎥\n", "⎢ 5 4 3⎥\n", "⎢\\Delta t \\Delta t \\Delta t ⎥\n", "⎢───────── ───────── ─────────⎥\n", "⎢ 12 4 2 ⎥\n", "⎢ ⎥\n", "⎢ 4 3 ⎥\n", "⎢\\Delta t \\Delta t 2⎥\n", "⎢───────── ───────── \\Delta t ⎥\n", "⎣ 6 2 ⎦" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Gs*Gs.T" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(9, 9)\n" ] } ], "source": [ "sj = 0.1\n", "\n", "Q = np.matrix([[(dt**6)/36, 0, 0, (dt**5)/12, 0, 0, (dt**4)/6, 0, 0],\n", " [0, (dt**6)/36, 0, 0, (dt**5)/12, 0, 0, (dt**4)/6, 0],\n", " [0, 0, (dt**6)/36, 0, 0, (dt**5)/12, 0, 0, (dt**4)/6],\n", " [(dt**5)/12, 0, 0, (dt**4)/4, 0, 0, (dt**3)/2, 0, 0],\n", " [0, (dt**5)/12, 0, 0, (dt**4)/4, 0, 0, (dt**3)/2, 0],\n", " [0, 0, (dt**5)/12, 0, 0, (dt**4)/4, 0, 0, (dt**3)/2],\n", " [(dt**4)/6, 0, 0, (dt**3)/2, 0, 0, (dt**2), 0, 0],\n", " [0, (dt**4)/6, 0, 0, (dt**3)/2, 0, 0, (dt**2), 0],\n", " [0, 0, (dt**4)/6, 0, 0, (dt**3)/2, 0, 0, (dt**2)]]) *sj**2\n", "\n", "print(Q.shape)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(6, 6))\n", "im = plt.imshow(Q, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n", "plt.title('Process Noise Covariance Matrix $Q$')\n", "ylocs, ylabels = plt.yticks()\n", "# set the locations of the yticks\n", "plt.yticks(np.arange(10))\n", "# set the locations and labels of the yticks\n", "plt.yticks(np.arange(9),('$x$', '$y$', '$z$', '$\\dot x$', '$\\dot y$', '$\\dot z$', '$\\ddot x$', '$\\ddot y$', '$\\ddot z$'), fontsize=22)\n", "\n", "xlocs, xlabels = plt.xticks()\n", "# set the locations of the yticks\n", "plt.xticks(np.arange(7))\n", "# set the locations and labels of the yticks\n", "plt.xticks(np.arange(9),('$x$', '$y$', '$z$', '$\\dot x$', '$\\dot y$', '$\\dot z$', '$\\ddot x$', '$\\ddot y$', '$\\ddot z$'), fontsize=22)\n", "\n", "plt.xlim([-0.5,8.5])\n", "plt.ylim([8.5, -0.5])\n", "\n", "from mpl_toolkits.axes_grid1 import make_axes_locatable\n", "divider = make_axes_locatable(plt.gca())\n", "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n", "plt.colorbar(im, cax=cax)\n", "\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Disturbance Control Matrix $B$" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0.]\n", " [0.]\n", " [0.]\n", " [0.]\n", " [0.]\n", " [0.]\n", " [0.]\n", " [0.]\n", " [0.]] (9, 1)\n" ] } ], "source": [ "B = np.matrix([[0.0],\n", " [0.0],\n", " [0.0],\n", " [0.0],\n", " [0.0],\n", " [0.0],\n", " [0.0],\n", " [0.0],\n", " [0.0]])\n", "print(B, B.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Control Input $u$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Assumed constant over time" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "u = 0.0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Identity Matrix" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1. 0. 0. 0. 0. 0. 0. 0. 0.]\n", " [0. 1. 0. 0. 0. 0. 0. 0. 0.]\n", " [0. 0. 1. 0. 0. 0. 0. 0. 0.]\n", " [0. 0. 0. 1. 0. 0. 0. 0. 0.]\n", " [0. 0. 0. 0. 1. 0. 0. 0. 0.]\n", " [0. 0. 0. 0. 0. 1. 0. 0. 0.]\n", " [0. 0. 0. 0. 0. 0. 1. 0. 0.]\n", " [0. 0. 0. 0. 0. 0. 0. 1. 0.]\n", " [0. 0. 0. 0. 0. 0. 0. 0. 1.]] (9, 9)\n" ] } ], "source": [ "I = np.eye(9)\n", "print(I, I.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Measurements" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Synthetically creation of the Position Data for the ball" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "Hz = 100.0 # Frequency of Vision System\n", "dt = 1.0/Hz\n", "T = 1.0 # s measuremnt time\n", "m = int(T/dt) # number of measurements\n", "\n", "px= 0.0 # x Position Start\n", "py= 0.0 # y Position Start\n", "pz= 1.0 # z Position Start\n", "\n", "vx = 10.0 # m/s Velocity at the beginning\n", "vy = 0.0 # m/s Velocity\n", "vz = 0.0 # m/s Velocity\n", "\n", "c = 0.1 # Drag Resistance Coefficient\n", "d = 0.9 # Damping\n", "\n", "Xr=[]\n", "Yr=[]\n", "Zr=[]\n", "for i in range(int(m)):\n", " accx = -c*vx**2 # Drag Resistance\n", " \n", " vx += accx*dt\n", " px += vx*dt\n", "\n", " accz = -9.806 + c*vz**2 # Gravitation + Drag\n", " vz += accz*dt\n", " pz += vz*dt\n", " \n", " if pz<0.01:\n", " vz=-vz*d\n", " pz+=0.02\n", " if vx<0.1:\n", " accx=0.0\n", " accz=0.0\n", " \n", " Xr.append(px)\n", " Yr.append(py)\n", " Zr.append(pz)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Add Noise to the Real Position" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "sp= 0.1 # Sigma for position noise\n", "\n", "Xm = Xr + sp * (np.random.randn(m))\n", "Ym = Yr + sp * (np.random.randn(m))\n", "Zm = Zr + sp * (np.random.randn(m))" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$$\\left ( -1.654374084508773, \\quad 2.8899045396613925\\right )$$" ], "text/plain": [ "(-1.654374084508773, 2.8899045396613925)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(16,9))\n", "ax = fig.add_subplot(111, projection='3d')\n", "ax.scatter(Xm, Ym, Zm, c='gray')\n", "ax.set_xlabel('X')\n", "ax.set_ylabel('Y')\n", "ax.set_zlabel('Z')\n", "plt.title('Ball Trajectory observed from Computer Vision System (with Noise)')\n", "\n", "#ax.w_xaxis.set_pane_color((1.0, 1.0, 1.0, 1.0))\n", "\n", "# Axis equal\n", "max_range = np.array([Xm.max()-Xm.min(), Ym.max()-Ym.min(), Zm.max()-Zm.min()]).max() / 3.0\n", "mean_x = Xm.mean()\n", "mean_y = Ym.mean()\n", "mean_z = Zm.mean()\n", "ax.set_xlim(mean_x - max_range, mean_x + max_range)\n", "ax.set_ylim(mean_y - max_range, mean_y + max_range)\n", "ax.set_zlim(mean_z - max_range, mean_z + max_range)\n", "#plt.savefig('BallTrajectory-Computervision.png', dpi=150, bbox_inches='tight')" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(3, 100)\n" ] } ], "source": [ "measurements = np.vstack((Xm,Ym,Zm))\n", "print(measurements.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Initial State" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0. ]\n", " [ 0. ]\n", " [ 1. ]\n", " [10. ]\n", " [ 0. ]\n", " [ 0. ]\n", " [ 0. ]\n", " [ 0. ]\n", " [-9.81]] (9, 1)\n" ] } ], "source": [ "x = np.matrix([0.0, 0.0, 1.0, 10.0, 0.0, 0.0, 0.0, 0.0, -9.81]).T\n", "print(x, x.shape)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "# Preallocation for Plotting\n", "xt = []\n", "yt = []\n", "zt = []\n", "dxt= []\n", "dyt= []\n", "dzt= []\n", "ddxt=[]\n", "ddyt=[]\n", "ddzt=[]\n", "Zx = []\n", "Zy = []\n", "Zz = []\n", "Px = []\n", "Py = []\n", "Pz = []\n", "Pdx= []\n", "Pdy= []\n", "Pdz= []\n", "Pddx=[]\n", "Pddy=[]\n", "Pddz=[]\n", "Kx = []\n", "Ky = []\n", "Kz = []\n", "Kdx= []\n", "Kdy= []\n", "Kdz= []\n", "Kddx=[]\n", "Kddy=[]\n", "Kddz=[]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Kalman Filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![Kalman Filter](Kalman-Filter-Step.png)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "hitplate=False\n", "for filterstep in range(m):\n", " \n", " # Model the direction switch, when hitting the plate\n", " if x[2]<0.01 and not hitplate:\n", " x[5]=-x[5]\n", " hitplate=True\n", " \n", " # Time Update (Prediction)\n", " # ========================\n", " # Project the state ahead\n", " x = A*x + B*u\n", " \n", " # Project the error covariance ahead\n", " P = A*P*A.T + Q \n", " \n", " \n", " # Measurement Update (Correction)\n", " # ===============================\n", " # Compute the Kalman Gain\n", " S = H*P*H.T + R\n", " K = (P*H.T) * np.linalg.pinv(S)\n", "\n", " \n", " # Update the estimate via z\n", " Z = measurements[:,filterstep].reshape(H.shape[0],1)\n", " y = Z - (H*x) # Innovation or Residual\n", " x = x + (K*y)\n", " \n", " # Update the error covariance\n", " P = (I - (K*H))*P\n", " \n", " \n", " \n", " # Save states for Plotting\n", " xt.append(float(x[0]))\n", " yt.append(float(x[1]))\n", " zt.append(float(x[2]))\n", " dxt.append(float(x[3]))\n", " dyt.append(float(x[4]))\n", " dzt.append(float(x[5]))\n", " ddxt.append(float(x[6]))\n", " ddyt.append(float(x[7]))\n", " ddzt.append(float(x[8]))\n", " \n", " Zx.append(float(Z[0]))\n", " Zy.append(float(Z[1]))\n", " Zz.append(float(Z[2]))\n", " Px.append(float(P[0,0]))\n", " Py.append(float(P[1,1]))\n", " Pz.append(float(P[2,2]))\n", " Pdx.append(float(P[3,3]))\n", " Pdy.append(float(P[4,4]))\n", " Pdz.append(float(P[5,5]))\n", " Pddx.append(float(P[6,6]))\n", " Pddy.append(float(P[7,7]))\n", " Pddz.append(float(P[8,8]))\n", " Kx.append(float(K[0,0]))\n", " Ky.append(float(K[1,0]))\n", " Kz.append(float(K[2,0]))\n", " Kdx.append(float(K[3,0]))\n", " Kdy.append(float(K[4,0]))\n", " Kdz.append(float(K[5,0]))\n", " Kddx.append(float(K[6,0]))\n", " Kddy.append(float(K[7,0]))\n", " Kddz.append(float(K[8,0]))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Plots" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimated State" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(16,9))\n", "plt.subplot(211)\n", "plt.title('Estimated State (elements from vector $x$)')\n", "plt.plot(range(len(measurements[0])),dxt, label='$\\dot x$')\n", "plt.plot(range(len(measurements[0])),dyt, label='$\\dot y$')\n", "plt.plot(range(len(measurements[0])),dzt, label='$\\dot z$')\n", "plt.legend(loc='best',prop={'size':22})\n", "\n", "plt.subplot(212)\n", "plt.plot(range(len(measurements[0])),ddxt, label='$\\ddot x$')\n", "plt.plot(range(len(measurements[0])),ddyt, label='$\\ddot y$')\n", "plt.plot(range(len(measurements[0])),ddzt, label='$\\ddot z$')\n", "\n", "plt.xlabel('Filter Step')\n", "plt.ylabel('')\n", "plt.legend(loc='best',prop={'size':22})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Uncertainty" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(16,9))\n", "plt.subplot(311)\n", "plt.plot(range(len(measurements[0])),Px, label='$x$')\n", "plt.plot(range(len(measurements[0])),Py, label='$y$')\n", "plt.plot(range(len(measurements[0])),Pz, label='$z$')\n", "plt.title('Uncertainty (Elements from Matrix $P$)')\n", "plt.legend(loc='best',prop={'size':22})\n", "plt.subplot(312)\n", "plt.plot(range(len(measurements[0])),Pdx, label='$\\dot x$')\n", "plt.plot(range(len(measurements[0])),Pdy, label='$\\dot y$')\n", "plt.plot(range(len(measurements[0])),Pdz, label='$\\dot z$')\n", "plt.legend(loc='best',prop={'size':22})\n", "\n", "plt.subplot(313)\n", "plt.plot(range(len(measurements[0])),Pddx, label='$\\ddot x$')\n", "plt.plot(range(len(measurements[0])),Pddy, label='$\\ddot y$')\n", "plt.plot(range(len(measurements[0])),Pddz, label='$\\ddot z$')\n", "\n", "plt.xlabel('Filter Step')\n", "plt.ylabel('')\n", "plt.legend(loc='best',prop={'size':22})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Kalman Gains" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(16,9))\n", "plt.plot(range(len(measurements[0])),Kx, label='Kalman Gain for $x$')\n", "plt.plot(range(len(measurements[0])),Ky, label='Kalman Gain for $y$')\n", "plt.plot(range(len(measurements[0])),Kz, label='Kalman Gain for $z$')\n", "plt.plot(range(len(measurements[0])),Kdx, label='Kalman Gain for $\\dot x$')\n", "plt.plot(range(len(measurements[0])),Kdy, label='Kalman Gain for $\\dot y$')\n", "plt.plot(range(len(measurements[0])),Kdz, label='Kalman Gain for $\\dot z$')\n", "plt.plot(range(len(measurements[0])),Kddx, label='Kalman Gain for $\\ddot x$')\n", "plt.plot(range(len(measurements[0])),Kddy, label='Kalman Gain for $\\ddot y$')\n", "plt.plot(range(len(measurements[0])),Kddz, label='Kalman Gain for $\\ddot z$')\n", "\n", "plt.xlabel('Filter Step')\n", "plt.ylabel('')\n", "plt.title('Kalman Gain (the lower, the more the measurement fullfill the prediction)')\n", "plt.legend(loc='best',prop={'size':18})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Covariance Matrix" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(6, 6))\n", "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n", "plt.title('Covariance Matrix $P$ (after %i Filtersteps)' % m)\n", "ylocs, ylabels = plt.yticks()\n", "# set the locations of the yticks\n", "plt.yticks(np.arange(10))\n", "# set the locations and labels of the yticks\n", "plt.yticks(np.arange(9),('$x$', '$y$', '$z$', '$\\dot x$', '$\\dot y$', '$\\dot z$', '$\\ddot x$', '$\\ddot y$', '$\\ddot z$'), fontsize=22)\n", "\n", "xlocs, xlabels = plt.xticks()\n", "# set the locations of the yticks\n", "plt.xticks(np.arange(7))\n", "# set the locations and labels of the yticks\n", "plt.xticks(np.arange(9),('$x$', '$y$', '$z$', '$\\dot x$', '$\\dot y$', '$\\dot z$', '$\\ddot x$', '$\\ddot y$', '$\\ddot z$'), fontsize=22)\n", "\n", "plt.xlim([-0.5,8.5])\n", "plt.ylim([8.5, -0.5])\n", "\n", "from mpl_toolkits.axes_grid1 import make_axes_locatable\n", "divider = make_axes_locatable(plt.gca())\n", "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n", "plt.colorbar(im, cax=cax)\n", "\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Position in x/z Plane" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(16,9))\n", "\n", "plt.plot(xt,zt, label='Kalman Filter Estimate')\n", "plt.scatter(Xm,Zm, label='Measurement', c='gray', s=30)\n", "plt.plot(Xr, Zr, label='Real')\n", "plt.title('Estimate of Ball Trajectory (Elements from State Vector $x$)')\n", "plt.legend(loc='best',prop={'size':22})\n", "plt.axhline(0, color='k')\n", "plt.axis('equal')\n", "plt.xlabel('X ($m$)')\n", "plt.ylabel('Y ($m$)')\n", "plt.ylim(0, 2);\n", "plt.savefig('Kalman-Filter-CA-Ball-StateEstimated.png', dpi=150, bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Position in 3D" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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efPFF1NTUyJeLooitW7eiq6sLe/fuxcGDB3HbbbeNu51sPNYSp9OJQCCAzs5OPPDAA7jyyisxNDSU9n5kairPpyT5vUiUd899G/jNF7L757lvZ3TT0WgUL774Is466ywAo8Pk9+/fj507d2LXrl1499138eqrrwIAfv3rX+Pdd9/F3//+d9xzzz3jnjgkdWBYJCLC6JnQqqoqVFRU4C9/+QtuuOEG+WcnnHACli5dCp1Oh2XLluHLX/4yXnnlFUX243vf+x6sVitKSkqg0+mwZcsWlJeXw2Kx4NZbb8W7776L4eHhMdf75S9/iauuugqrV6+GXq/HZZddBmA0RL755pvo7+/Hj3/8Y5SWlqKkpATHHntsytsPh8N4/PHH8aMf/Qjl5eWYN28errvuOjzyyCPy79hsNlx55ZXQ6/UoKSnBV77yFTz66KNyteyRRx4ZN9T+4he/wM0334yFCxfCYDBg69at2LlzJzo6OmA0GjE0NIR9+/YBAFpbW9HY2JjxY3fCCSfIoWXz5s1wuVz4f//v/8FgMOCCCy7AJ598Ap/PBwDYuHEj5s2bB0EQ8LnPfQ4nnXRS2slyfvGLX+D2229HU1OT/Fw8/vjjiMVieOKJJ3D22Wfj2GOPhdlsxu233y4/Fqkcf/zxeOWVV9DR0QGLxYIvfelLeOWVV7B//36MjIxgyZIlGd/nTZs2YdWqVTAajbjooouwa9eutL///PPP4/zzz0dlZWXC5UceeSROOukkmEwm1NfX47rrrkv7Gs/mY22xWLB161YYjUacddZZMJvN+Oc//znubV911VWoqqpCVVUVjj766EwepjHSPZ+S+PciUbEKBAJob29HbW0tXC4XTjnlFACjnyXPP/88VqxYgZUrV2Lfvn3ySa977rkHy5cvx9q1a+FwOOTLSZ0M+d4BIqJC8NRTT+Hkk09GNBrF9u3bsWHDBuzduxeNjY14++238e1vfxt79uxBKBTCyMgINm/erMh+tLS0yP+ORqO46aab8OSTT6K/vx863ej5vf7+fpSWliZc7/Dhw/j973+Pu+++W74sFAqho6MDkUgEc+bMgV6vn/D2e3t7EY1GMXv2bPmy2bNnJww9it9HADj22GNhMBjwt7/9DdXV1bDb7fjCF76QcvuHDx/Gv//7v+Paa6+VL9PpdHA6nTj11FNxxRVX4Morr4TD4cC5556LO+64A+Xl5RPuNzBawZKUlJRgxowZ8mMmHfD7fD6UlZXh2WefxW233Yb9+/cjFovB7/en7X2z2+3YuHGjvD0AEAQBvb296OzsTHhMysrKEqp2yTZs2IDnn38edXV1OP7443HCCSfgiSeeADAaJOMnoplIfJi2Wq1yQBvPjh078PnPfx7V1dW49NJL5cu7u7txzTXX4PXXX4fX60UsFpOHqKaSzce6rq4u4bU50f24//77sWXLlrT3cyLpnk9J8uucKO/OGH+Iu1KknsXBwUGceeaZuO+++3DNNddAFEXcdNNN+MY3vpHw+y+//DJeeOEFvPnmm7BarTjhhBMQDAZzvt+UPawsEhHF0ev1OOecc6DX6/G3v/0NAHDhhRfirLPOgsPhwODgIK644oq0laPpiA8KDz/8MP70pz/hpZdewuDgID755BMASHnbLS0tuOWWW+DxeOQ/fr8f5513HlpaWnD48GFEo9G0twcA9fX10Ov1OHz4sHyZ3W5HU1PTuNcBgEsvvRS/+93v8Mgjj+C8886D2WxOef9aWlrw4IMPJuxnIBDAmjVrAADf+ta38N5772HPnj3Yu3cv7rrrrnFvc6oCgQA2bdqEm266CT09PfB4PDj11FPlxzXVbTU3N+Mvf/lLwn4Hg0E0NjZi5syZCbPn+nw+uFyucW9/w4YNePXVV/HKK69gw4YNWL9+PV577TX5/6lk6/6vX78e27dvx1VXXYXHHntMvvzGG2+E2WzGhx9+iKGhITz00ENZeY1P9FjnwmSfz3TXIypWlZWVuOeee3DnnXciHA7jtNNOw69//Wv5xE5HRwd6e3sxODiI6upqWK1W7Nu3D2+99Vae95ymi2GRiCiOKIrYvn073G43Fi9eDADwer2oqamBxWLBzp078eijj+ZkX7xeL8xmM2pra+H3+/Gd73xn3N/9+te/jvvuuw/vvPMOYrEYPB4PnnzySXR2dmLp0qWoqanBjTfeiMHBQfh8PjkINzQ0wOl0IhwOAwCMRiM2bdok9wd++umnuPvuu3HxxRen3ddLLrkETz75JB599NGEilWyK664Aj/84Q/lCXGk/QSAnTt3YufOnYhEIigtLYXJZJIrTg0NDTh48GDmD14aIyMjCIVCmDFjBvR6PZ599lm8+OKL8s8bGhrQ398Pr9ebsN8333yzvI5fb28vnn76aQDA5s2bsX37drz55psYGRnB1q1b0waNxYsXQ6/X449//COOP/54VFdXo7q6Wq5op5L8PE3H5z73OTz55JO4/PLL5d5br9eL0tJSVFZWwuFw4M4775z27QATP9a5MNnnk4hSW7FiBZYvX44//vGPOPXUU3HhhRdi3bp1WLp0KTZt2gSv14vTTz8dkUgEy5Ytw3/+538m9P+TOjEsEhFhtK+qrKwMFRUV+M53voPf/va3aGtrAzA67O273/0uysvL8f3vfx/nnXdeTvbp3/7t3zBr1izMmjULbW1tOOaYY8b93aOPPhr33XcfrrjiCtTU1GDx4sX4wx/+AFEUIQgC/vCHP+Cjjz7C3LlzMWfOHDz66KMYHBzE2rVrMW/ePDQ0NKCxsRHRaBT33nsvTCYT5s6diw0bNuArX/lK2gAIjK6ftXTpUphMprT7uXnzZlx//fXYvHkzKioqsGzZMvzf//0fgNHgePnll6Oqqgpz5szBzJkzcd111wEAvvrVr+KDDz5AdXU1Nm3aNIVH8zNVVVW4++678aUvfQk1NTV48sknceaZZ8o/X7JkCc4991zMmTMHVVVV6O3txfXXX4/TTz8dJ510EsrLy3HMMcfgnXfeAQAsW7YMP//5z3HeeeehqakJjY2NE/ZaHn/88aivr5dnQt2wYQN0Oh2WL1+e8vdPOeUULFiwQH6epuv000/Ho48+iosvvhh/+tOf8L3vfQ87d+5EZWUlzjrrLJx77rnTvg1g4sc6Fyb7fBLRZ5KHhD/zzDNyT7o0q/aHH36IN998E0cccQTMZjOee+457N69G0888QRefvlleY3YQ4cOJczmTOogTDAUJHfjRIiIaFIuvPBCtLW14cYbb0QkEkkYRikIAiKRCCKRSEJflkT6XVEU5T/x1TBBEKDT6aDX6+W/pcuk7Se79NJLMW/ePEWWFiEiKkYff/yxPMqFKBvGeU2NOxyGE9wQEamMKIoIh8PYt28fTjvtNITDYTnAZdpnJf3eeL8viiJisZjc55gcJqUAKYXJQ4cOYfv27QlLIhAREZG6cRgqEZFKiKKISCSCkZER1NfXo66uDl/84hfHrfZNZ4KO+MqiXq+HwWBICIfSvgSDQdx444046qijcN1116GyshJDQ0Pw+XwIBAIIhUIIh8OIRqM5ndSEiIiIpo/DUImICpg0RDQSichVvkwriNFoFOFwOOUwVKUkD29NlhxCdTqd/Ef6ORERjfr444+xaNEifjZSVoiiiH379nEYKhGR2omiiGg0mrIXsZClG94q3Q9peGvy0NahoSGUlpaipKQk4z5JIiIts1gsGBgYQG1tLT8DaVpEUcTAwAAsFsukrsewSERUIMarIuayMqikiYJkb2+vvM5jKuNVJBkkiUirmpub4XQ60dfXl+9dIQ2wWCxobm6e1HUYFomI8iy+itjb2wuv14sjjjiiqAJQ/AQ9qcJifJBOtdagFBzjw2R8VZKISI2MRiPmzp2b792gIsawSESUB+mqiLFYrCgDjiAI406Ck656KF1HCtyprpuuKklERESpMSwSEeXQRL2I0kyj2aC2IJQuLE50vfi/46XrkxRFMaEiyT5JIiKiRAyLREQKm0wvoiAIiMViud5FzZrOhDsA+ySJiKi4MSwSESlkKjOaZrOyqDZTrSxO5/bi/07GPkkiIip2DItERFk03RlNpZ5Fyr/p9knGD21lnyQREakRwyIRURZka13EYh6GmuvK4nRkMrw1/vUQ/3vxE+7E/x0/IywREVEhYFgkIpoiJdZFLObKoprCYjrT7ZNMV5FkkCQiolxiWCQimqRsVRFTyXZgYrgoLJn0ScZiMcRisXH7JJMn3GGfJBERKYVhkYgoA0pUEVNhZVH9lcXpyKRPcqIJd9gnSURE2cKwSESURnxAzHYVMZVsz4aaapgjqVO2+iQFQYDBYGCfJBERTYhhkYgoSa6qiKlkc4IbtYUAVhanbjJ9ku+++y6OOuqohN9hnyQREaXCsEhE9C+5riKmwmGoDIvZlhwkpWU9JFKfZDQaZZ8kERElYFgkoqKWzypiKtkehko0kWz1SRoMBvm9wyBJRKQNDItEVJQKoYqYSjFX14r5vheqyfRJhkKhMdflepJEROrGsEhERaPQqoiUiGFRXbK5nqQ08Q77JImICgvDIhFpXqFWEYm0KtP1JKU+yeQwmapPkkGSiCj3GBaJSJNYRVQfVhaVVyiP70R9ktJ7N12fZHJFkn2SRETZx7BIRJrCKiLR+NSw7mYmE+5IfZKprss+SSKi7GFYJCLVix/SxiqiemVzjUnSpun0ScZXINknSUSUGYZFIlItVhG1hcNQlaeGyuJUsU+SiCj7GBaJSFWkA77BwUEAQElJCauIRJNQrMGHfZJERJPHsEhEqpBcRezp6YHZbEZpaWm+d42yhJVF5fHxTS1bfZLJVUnp50REasWwSEQFK10vosFg0Gx/mxSaeJBJ2cbX1eRNp0/S4/GgoqICFotFDpTskyQiNWFYJKKCk0kvok6nkwOk1kgTvej1+qxsSy1YWSS1mShIdnV1wWw2y1VG9kkSkdowLBJRQZjsjKY6nS5lb5EW6HS6ogxNDIvKY2Uxd6TXsxQGk43XJyk9R8l9klKIZJ8kEeUSwyIR5dVUZzTV6/WarSzqdDrNDrGdCMOi8hg0cicWi417wkupPkk+v0SUTQyLRJRz2VgXsRiGoWaDmipJatlPNWMYz610YTGdqfZJiqKYUJFknyQRTRfDIhHlTDbXRdTr9ZqtvhVrZZHDUJWnppMHWjDVsJjOZIJkKuyTJKLJYFgkIkVlo4qYipYDVTZDE2dWpWR8LeSOEmExnXRBEpj8epLskyQihkUiUkQ2q4ipsGdxYmo7uGNlUXl8fHOvkN6H0+2TjB/ayj5JouLAsEhEWSNVESORiBx2slFFTEXLlcVinQ0VYJhRGqvMNJ5MhrdKQZJ9kkTFg2GRiKZN6SpiKlquLGZzghs14QElUWGa6oQ7EvZJEqkXwyIRTUkuq4ipaL2yqNX7lg6HoSqPlUXKtmz0SSYPb2WfJFHhYFgkoknJRxUxFS1XFot5GCopjwfglEuZ9ElKQ1uTxVch2SdJlB8Mi0Q0oXxXEVPRcvWtmIehMiQri48vFZKp9klK1xmvKsnhrUTZw7BIROMqlCpiKoWwD0rJZmVRTQFMTfuqVhyGmjt8LU/PVPsk+/v7UVZWhtLS0nErknwPEGWOYZGIEhRiFbHYFGtlkUhLGMyVky5IulwulJSUyEEyXZ9kfJBknyRRagyLRASgsKuIxUbLQ2zTYWVReQwwuROLxXiSLQ+i0SgMBsO4j318n+R4QVL6YzAY5BDJIEnFimGRqIixiliYinWCG4bF3OABb24wLOZHJBKBwTD+4e1k+iRHRkbYJ0lFj2GRqAixiljYOAyVlMIwnjsMi/kRjUah1+undN3pricZHyL1en3C0FZ+v5JaMSwSFQmtVhG1OKxOp9NlZVkQURQxODgIURRhtVphNBqzsHfKYWVReVp8vxSqWCzGxzoPlArpmawnGd8nmfxeS9UnySBJasCwSKRxWq4iSr19Uz2LXKh0Oh0ikciUrx+JRNDZ2Qmn0wmr1QpBEBAIBBCJRKDT6WC1WlFSUoKSkhL534UeJCk7GBZzRxRF1Z+MU6N8vcYnWk9S+i5O1yeZXJFknyQVAoZFIg2SznBKZzcBbVQRk+n1+mkNOSpUUx2G6vV6Ybet3aqaAAAgAElEQVTb4fF4MGvWLKxatQp6vR6RSEQ+4IhGowgEAvD7/QgEAnC73XKQ1Ov1Y0Kk1WpN2/+TTawskpZwGCpJJgqSwGd9kqmuyz5JyieGRSINia8iOhwOAEBLS4tmv0y0OmvoZCa4icVi6OnpgcPhgF6vh81mQ2trq/ycJx986PV6lJWVoaysbMy24oOk3++Hy+XKaZBkWFQeK4u5w7CYH2p7fU+nTzK+Ask+SVIKwyKRyo3Xi2gwGBAKhTT9ZaHX6zUZFjOpLAYCATidTvT09GDGjBlYsmQJrFZryt/NNCBMFCSlaqQUJP1+v1zZTQ6RJSUlOatIEhUihsXc09rJJvZJUiHgNzmRSk3UiygNP9SybE0EU2jGq5iKooiBgQHY7XaEw2G0tLTgmGOOyckBqV6vR3l5OcrLy8f8LBKJIBAITDtIsrKoPFYWc4dhMfe02JaQDvskKRcYFolUZDIzmkr9fFpWLMNQw+EwOjo60NnZiYqKCsyfPx8VFRV53MNEBoMh4yA5MDCAQCAwJkharVbNPp+FhGExdxgWc6/YwmI62eqTTK5KSj+n4sGwSKQCU5nR1GAwaD4sajUQS8NQBwcH4XA4MDQ0hFmzZmH16tWqm7U0kyAp9Uh6vV4MDg5i586d0Ov1Y6qRHNpKasKlM3KPYTEz2eiTjJ9wh32S2sZvXaICNd11EYtlGKrWKlHRaBQDAwPo7u7GyMgIbDYb2trapvwFXMhf3MlBcmRkBPv27cPy5cvHBMn+/v6EimRykLRarTxIzAAri7mjxWV9Ch3D4vRNpk9S+r/0u319fairq4PJZGKfpIYwLBIVGOlDeLrrImq16hZPS/fR7/fD4XCgr68P1dXVqKmpQXt7e753K28mqkhKk+0MDw8nBEmDwZAwa6sUJnkASbnGymLuRSIRjj5QWLrjEYfDgbq6OvZJagzfUUQFYLpVxFSKYRiq2iuLoiiir68PDocD0WgUNpsNCxYsgN/vx4EDB/K9ezmX6QQ3BoMBFRUVKfs2w+Gw3CM5XpBMrkoWU5BkZTF3RFFkz2KOsbKYf+OFdfZJqhfDIlEeZauKmEoxDENVa2UxFArB6XSiq6sL1dXVWLhwYcJyFZNZZ1FLsjEbqtFohNFoTBsk/X6/HCT9fj9isVhCkIzvkdTagSfDYu5IryvKHYbFwjXVPklRFOH1enHvvffiJz/5Se52mGT8FCPKMSWqiKmoveqWCTXdR1EUMTg4CLvdjuHhYTQ1NWHNmjUpDybVdL/UJNMg6fP50Nvbi0AgIB/wp5pshwellA5nQ809hsX8mc6JvomC5MDAAD755JMpb5+mh2GRKEeSq4hSBVGps/zFUD3Q6/UYGRnJ926kFYlE0NXVBafTCavVCpvNhqqqqrTPjzQbarHJ5zqLxRIkWVnMHYbF3JOGm1PuKRXUBUGAy+VCTU1N1rdNmeE7ikhBuaoiFqtCrsD5fD44HA64XC40NjZi5cqVMJvNGV23WIehFqqJgqQ02Y7X600IkkajcUyPpMViyWuQZFjMHYbF3ItEIrBYLPnejaIUDocVW9ppYGAAtbW1imybJsawSKSAXFcRi1WhhcVYLIa+vj7Y7XYIggCbzYaFCxdO+oAxm5VFNb3m8llZnCqj0YjKykpUVlaO+ZnagiRlF8Ni7nEYav4oOROty+ViWMwjhkWiLCnUKqKWKwmFMsFNMBiE0+lEd3c36urq0NraitLS0ilvr9BCcK6oMSymM16QFEVRXv7D7/enDJLxQ1qlf2fjs0TLnweFhmEx9xgW80fJyqLb7UZ9fb0i26aJMSwSTVMhVxH1er2mF4bOZ6gSRRFutxt2ux3BYBDNzc1Yt25dVh5rrYUmSiQIQtogGd8j6fV60dPTg2AwOCZIxgdKhpLCw7CYewyL+aNkZdHtdmPx4sWKbJsmxrBINAWFWkVMJi2fodUvz3xUFiORCDo7O+F0OlFeXo65c+emHII4HYVwoiEfGJJHHwOTyQSTyTRhkBwaGkJ3d/ekgiQri7kTi8X4WOcYw2L+KFlZ5DDU/GJYJJqEQq4iplIowzSVksvKotfrhd1uh8fjwaxZs7Bq1SqYTKac3DYRMLkgOTg4mBAkTSYTSkpKEAqFYDabMTw8zIqkwkRR5OObY1o+OVrowuEwrFarIttmWMwvhkWiCailipiKwWDQdFhUOgzHYjH09PTAbrfDYDDAZrOhtbW1YE8OqB0f16nLJEj6/X50dHQgEAjg008/RSAQgCiKcpBMnmxHDZ9xhYzDUHOPS2fkj5LDUD0eD+rq6hTZNk2M7yiicaitipiKNAxVq5SqLAYCATidTvT09KC+vh5Lly5V7IxpLqjpNUvZFx8kvV4vDAYDZs6cCSAxSMZXJOODZPJkOwySmWFYzD0O/c0fJYehejweVFdXK7JtmhjDIlEcNVcRU9H6MNRs3j9RFDEwMAC73Y5wOIyWlhYcc8wxqn3uiTIRHySrqqoSfiaKIkKhUMLQ1q6uLgSDwTFBUvqbQfIzDIu5p7YTulqiVGVROi5jxTh/+MgTQRtVxFS0Pgw1G5XFcDiMjo4OdHZ2oqKiAvPnz0+5+LqacVITkkzmtSAIAsxmM8xm84RB0uPxoLOzUw6SZrN5zNIfxRYkGRZzr9gnyMonJSuLAEfI5BPDIhUtrVURUymGYahTPTgYHByEw+HA0NAQZs2ahdWrVyv6RZcvWjjpQdmTrRMHmQRJv9+PQCAAt9udMkjGD2/VapDke4+KhVIz0YZCIU1+N6sJwyIVHa1WEVPR+jDUyYpGo+ju7obD4YDZbIbNZkNbW5smn3ui8Sj9eo8Pksl9RpMNklarFWazWZNBkrKLldz8U+KzxeVysV8xzxgWqSjEVxHdbjf6+vqwYMECzX+xGAwGBIPBfO9G3vn9fjgcDvT19aGhoQHt7e2wWCz53q0JcfgoZVu+h+lNN0immmyH7xECuMaiVnHZjPxjWCRNS1VF1Ol0GBkZKYoDDK0PQ01HFEX09fXB4XAgFouhpaVFVScIpCG2xfA6pdwp5NfUREFyZGRE7pF0u93o6OjAyMjImCAZ3yNZqPeVso9hMX+UnIV2YGAANTU1imybMsOwSJozUS+i0WgsmgBVjMNQQ6EQnE4nurq6UF1djYULF6KsrCzfuzVpgiBwWBXRvwiCAIvFAovFMmGQdLlc8Pv9cpC0WCwpJ9thkNQWhsX8UXKNRbfbzcpinjEskmZk2otoNBoRDofztJe5pfXZUCWxWEyesGZ4eBhNTU1Ys2aNqqfaVmoNSSpuhVxZnKpMgqQ0tHW8IJk82Y7WHqNiwLCYP0rOhMqwmH/qPZIiwtRmNDUYDKwsakQkEkE4HMbbb78Nq9UKm82GqqoqTRzoTWemV6J0tPD+yFR8kEyWHCQHBgYQCATkPu/kIClNtpPJ48f3bu5FIhGGxTxRsrLocrlwxBFHKLJtygzDIqnSdGY0LaYDJa32LPp8PjgcDrhcLgDAsmXLUFpamue9yi5pGCpRNjHEfGaiIBkMBhEIBOQg6XQ6EQwG5d7KdEFSixXcQheNRlU9mkTNlKwsulwuHH300YpsmzLDdxWpRjGsi5htWqosxmIx9Pb2wuFwQBAE2Gw2LFq0CO+++64mDxBYWSQlMMRkRhAEeVhqsvgg6ff7UwZJi8WCcDgMt9uNkpKSjCuSNHUchpo/7FnUNu0dYZHmFNO6iNmmhSG3wWAQTqcTPT09qK2tRWtra0IVUUuBOB57FokKU3yQTJ6lUQqSQ0NDcLlc6O/vl3skpSCZPGsrg2R2MCzmj9KVxbq6OkW2TZlhWKSCpHQVUafTFcUXi1qrU6Iowu12w263IxgMorm5GWvXrk35fGk1VHEYKimBlUVlSUFSEARYrVYsWLBA/lksFkvokUwOksmztlqtVphMJj5fGYpGozCZTPnejaIUiUQUW7uYlcX8Y1ikgpKrKqJUcdN6WFSbSCSCjo4OdHR0oLy8HHPnzkVlZWXa62g1LKo16FPhY/hQXqplb3Q63bhDW5ODZF9fHwKBwJggGV+VZJBMFIlEUj62pDwlK4vDw8MoLy9XZNuUGYZFyrt89CJKYdFsNit2G5Q5r9cLu90Oj8eDWbNmYdWqVRmfIdbqMFRWFkkJPAGRG5NdpHyiIBk/2Q6DZGqc4CZ/lOpZlD6viu21XGj4rqK8yWcvohZ6+dQuFouhp6cHdrsdBoMBNpsNra2tk37+tVxZzNb94hctSTgMNTdEUcxq24Q0LDVZfJD0+/0pg2T8GpJaDpLF0FpSqJSqLDIsFgaGRcqpQpnR1Gg0IhwO5/Q286mQDhADgQAcDgd6e3tRX1+PpUuXpjwIypSWK4usApESCuWzQMtSDUNVQnyQTO7rShUk/X4/QqHQmCAp/a3mIMmwmD9KVRaHh4dRVlaW9e3S5DAsUk4U2oymxVRZNBgMeR+eI4oiBgYGYLfbEQ6H0dLSgvnz52flYIqVRaLM8QREbuQqLKaTSZCUeiR7e3sTgqRUiYyfbMdoNBZ0kGRYzB+lHvuBgQFUV1dnfbs0OQyLpJhCqSKmUkxhUa/XK7oGUjrhcBgdHR3o7OxERUUF5s+fj4qKiqzehlYri9mc4KaQKsuZUNv+qgkf29wohLCYTiZDW6Ug2dPTg0AgMCZIxlclCyFIctI67XG5XJwJtQAwLFLWFVoVMRWDwVA0w1DzEaYGBwdht9vh9XrR1NSE1atXKzZTmlYrcFq9X0TFoNDDYjoTBUlpop2JgqQUJnMVJFlZzA8lT0C5XK4xa5lS7jEsUlYUchUxFaPRCL/fn+/dyAlpGKrSotEouru74XA4YDabYbPZUFNTo/hBgk6n02SVOFuzoUonatRSUVLTvqoRH9vcUHNYTEen06G0tBSlpaVjfhYfJP1+P7q7u+H3+xEOh6HT6VL2SGYzSGZzUiHKXDQaVexxZ2WxMDAs0rSooYqYSrENQ1UyLPr9fjgcDvT19aGhoQHt7e2KLc6bil6vRygUytnt5QrXWSQlMCzmhlbDYjqFHCRJOZFIRLGRQ263m5XFAsCwSJOmtipiKsUWFrN9X0VRRF9fHxwOB2KxGFpaWrBgwYK8vAb0er0mh2sW6zqLnAWWtKAYw2I60wmSqSbbMRgMY4Ikg2V+hMNhxeZEcLvdmD17tiLbpswxLFLG1FpFTKXYwmK2KouhUAhOpxNdXV2orq7GwoUL8z6ttU6n0+wEN8XSVxuPYVFZrCzmRiwWY/9chtIFyWg0mjDZTldXFwKBQMogGYlEFFvvj8anZGWRw1ALA8MipaWFKmIqxRQWp3tfRVGEx+OBw+HA8PAwmpqasGbNmrwuxRFPqxPBMDQRqRf757JDr9dnFCSHh4cRiUSwZ8+eMUEyedZWyi4lK4sMi4WhMI72qOBoqYqYSjGFxalWFiORCLq6uuB0OmG1WmGz2VBVVVVwrwEtL52hxRA8EYZkZbGymBschqq8+CBZWVkJj8eD9vZ2AKNBMn7WVo/HA7/fj0gkIgfJVD2SNHlK9yzW1dUpsm3KHMMiybRaRUylmCYPmewEMD6fDw6HAy6XC42NjVi5ciXMZrOCezg9Wg1VxfQapdxhWMwNhsXcSl42Q6/Xo6ysLGWbRHyQ9Pv9DJLTFA6HFTtGcLvdrCwWAIZFkgOiVJ3RWhWx2GWydEYsFkNvby8cDgcEQYDNZsOiRYtU8RrQamWRE9wQqRfDYm5NZo3FyQRJt9uNQCAgB0kpPDJIfiYSiSg2d4GSQZQyx7BYpERRlIeZhkIhvP/++zj66KNVEQ5octLNhhoMBuF0OtHd3Y26ujq0tram7A0pZFquLE73fvn9fhw+fBj9/f0QBAEGgyFhsWzp70I6qGVYVBYri7nBsJhbkwmL6WQSJKXJduKDpF6vT9kjWSi9/UpSalIhfg8UDu2/iimB1IsohQfpADIajRbdAYRUudH6F3py5U0URbjdbtjtdgSDQTQ3N2PdunWqnblPq0tnTHUYqiiKGBgYwOHDhxGLxWCz2XDEEUdAFEVEIhH5YMfr9aKnpweBQACiKMJsNidMTW+1WmE2m4vuc6EY8DlVXjF8txQSKbApKdMg6ff74XK5iiZIRiIRRe5LNBqFTqfj51UB0MYrldKKryLG9yJKb8BifSMajUZEIhGYTKZ874qipJMBkUgEHR0d6OjoQHl5OebOnYvKysp87960aXXpjMkOQ41EIujs7ITT6URFRQWOPPJIlJeXAxg98yuKIoxGI4xGIyoqKhKuK4oiQqFQwoGO0+lEMBiEIAjygtnxVUmlFsxmZVFZfGxzg2Ext6LRaF7D10RBUqpGSp+vfr9froam6pFUU5BUqrLo8Xg0cYyiBep5NdKkpaoiputFLLbhSQaDAeFwWPNhURou8/bbb2PWrFlYtWqVpu6zloehZnJg7/f7YbfbMTAwMOXnVxAEmM1mmM1mVFdXJ/wsFoshGAyOu2B2/EGO9Gc6Z/gZFpVVbJ/z+cKwmFvZGoaqBL1ej/LycvnkXTxptIeag6RSlUUum1E4CusVR9M2URVxPNJQxUL7EFKSlpfPiMVi6Onpgd1uh16vh8FgwDHHHKPJg0Qt3icgfQgWRREulwuHDx9GJBKBzWbDkUceqcjBqRQIrVbrmC/u5KFXAwMDCAQC8mdJfIC0Wq2wWCw8gKaiEIvFNPvZVIgKOSymYzAYMg6S8Z+v8UEyftKdfB3DKfFad7lcqKmpyfp2afKKJxlomCiKckjMtIqYzGg0KrqwaiHSYlgMBAJwOBzo7e1FfX09li5dCovFgrfffpsHLiqTahhq8lDTBQsWpDzIyJV0Q6/C4bAcIoeGhtDd3Z3QH5k80Y7UH8nKorJYWcwNURR5YiSHIpEISkpK8r0bWZVJkJQ+Y/v7+xOCZHI1shArkhMZGBhgZbFAqOuVQwmmWkVMRQqLWvuwTUfqWVQ7aUITu92OcDiMlpYWzJ8/P+FAhQff6hM/DDV+qOnMmTMnPdQ0H+HAaDSisrJyTM9Jcn/kwMAAnE4nRkZGAAChUAgOhwMVFRVyoCz2qemziWExNzgMNbfUWlmcqmwGyem0Dih5bOHxeBgWCwTDospko4qYihQWi4ler1f1fQ6Hw+jo6EBnZycqKysxf/78MROXkLoFg0G89957ig81zaWJ+iM//PBDlJWVIRKJJPRHJg+7kg50iukAkdSDYTG3ii0spjNRkJQm2xkeHk4IkgaDIWHW1kw+Y5XqVwQg9+FT/jEsqkQ2q4ipFGNYVOt9HhwchN1uh9frRVNTE1avXs3Ki4ZEo1F0dnbCbrcjFAqhra0tKycB1FBR0ul0ckUyeWhrcn9k/EGO0WgcM6yV/ZGpqeF1oAUMi7lVbHMuTJXBYEBFRUXK75RwOCz3SI4XJJOrkkrNhAoAbrcbS5cuVWTbNDl8Z6lIOBzOShUxFZPJhFAolNVtFjqDwYBAIJDv3chINBpFd3c3HA4HzGYzbDYbampqeNAXR+0HwYFAAHa7Hf39/WhsbMSKFSuwZ88eVov/JdP+yMHBwYT+SIvFMqYiaTKZVP1aIXXgayx3WFmcvvGWVgI+C5J+v18OktKoj2g0io8//njMZDvTfT44G2rhYFhUCUEQoNfrFRsfbjQaMTw8rMi2C5UaJrjx+/1wOBzo6+tDY2Mj2tvbYbFYJr0dabIUrZ7pVutsvqIowu124/DhwwiFQpg9ezYWLFggrx2pxSVBJjKVCW7S9UeOjIzIw66kA5yRkREIgpByWKvWq/RqP6lClArDorLGC5IDAwMYGBhAY2Mj/H4/fD4fent7EQgEEIvF5FmxkyfbyeS5crvdDIsFQl1HVqQYtQ7JnI5CDYuiKKKvrw92ux2iKKKlpUUOEFMlhSmthkW1rbUYjUbR1dUFh8OBsrIyzJs3b0zQyXSdRRqfIAiwWCwpT7BI60dKFUmPxwO/349IJDJmEgit9UcyLJLWSO9byq1wOAyz2Tzh0NZMgmQsFkNZWRlKS0sBMCwWEoZFFVFySvliDIuFdp9DoRCcTie6urpQXV2NRYsWpRxyNxUGg0Hu7dIivV6virCYPNR05cqVMJvNKX83m+93NYWDXC2dEb9+ZLL42QTjh1zFYrGE/sj49SPV9BiT8niiJ7disRjDYh5EIpG0xxUTDW2VRn14vV785S9/wW9+8xuMjIygsrISPp8PDz30EI488kgsWLAA8+bNm9LIKonD4cCll16K7u5u6HQ6fP3rX8e111475e0VE4ZFAlB4wSkXCqGyKIoiPB4PHA4HhoeH0dTUhDVr1mR9OKVer8/7fVWSNGyzECUPNbXZbNOuFGtZIayzON5sgqIoJpwp93g86OzsRDAYBICU60eyP5IoN/g+y71wOCxXAicruX3gG9/4Br7xjW8AAHp6enDuueeisbER7733Hh5//HEcOHAAwWAQdXV1mD9/Pr773e9OarZUg8GAn/70p1i5ciW8Xi+OOuoonHLKKWhtbZ3S/hcThkUVUfKDkGExtyKRCLq6uuB0OmG1WmGz2VBVVaXYcywNQ9WqQhyGGj/UtLS0NOVQU1IXQRBgMplgMpnS9kf6/X709fUhEAhgZGQEOp1uzJT0VqtVdT22lDkGl9zK9wmmYjVRZXGq6uvrIQgCLrnkkoTLRVGEy+XC/v37J/19OnPmTMycORMAUF5ejsWLF6Ojo4NhMQP8piIA2g8TqeSjJ8zn88HhcMDlck04DDGbtP78FtL9CwaDsNvt6OvrQ0NDQ86eY60ohMriVMT3R9bU1CT8LBaLydXIQCCQsj8yeaIdVp7VS42vX6KpCIfDipz0CgaDKb83BUFAbW3ttHsZDx06hPfffx9r1qyZ1naKBcOiiih5ppJnQZUTi8XQ29sLh8MBQRBgs9mwaNGinD7mhTDkVkn5rixKw4kPHz6MkZERtLS0YP78+TzgnwK1hsV0dDodSktLUw7Xiu+PTJ4AwmQypVw/kp/XhY0zzuYWH+/8Uaqy6HK5UF1dnfXtAqMn7c8991z87Gc/49JUGWJYpAT80M2eYDAIp9OJ7u5u1NXVobW1dcpj+6erkCpvSsjX/ZPWv7Tb7SgtLcWcOXNQVVWV8/0g9ZqoP1Ia1up2uxP6I1OtH2k0Gvn5XQC0vExRIdLyTN+FLhwOKxYWk0doZEM4HMa5556Liy66COecc07Wt69VDIsqovRBgFrXqpuObK8/KE1mYrfbEQwG0dzcjHXr1uV9ljZpNlStynVlkUNNlaPFyuJUxPdHJp+AEEVRXvYjEAigt7cXfr8foVBI7o9MHtZaTJ/r+cawmFvFdtxSSJR6rbtcrqwvmyGKIi6//HIsXrwY119/fVa3rXV8d5FMmuSmmD50peGZJpNpWtuJRCLo6OhAR0cHysvLMXfu3IKazESv12t6AqNcVBbjh5oGg0HYbDbVDDVltUlbBEGQJ8xJFo1GE9aPdLlc8Pv98gG1dKIjfpFsNbyG1YRhMbei0WjeT8gWMyW+X5QIi6+//joeeeQRLF26FO3t7QCA22+/HZ///OezejtaVDypQAOUPuCTwmKqAxCtmm5Y9Hq9sNvt8Hg8mDVrFlatWjXt4KkEvV4vD1/TIiUri7FYTJ7VtKSkJOdDTYttaDgri9Oj1+vT9kf+/e9/h8lkgtfrTeiPNJvNYyqSZrO5qF572cKwmFsMi9qjxDDU4447jt8tU8SwSLJiXD5jKvc5Fouhu7sbDocDRqMRLS0taG1tLeiDqmLoWcx2WAwGg3A4HOjt7UV9fT3a29untSDwVEjBqZBfW9nGsKgcg8EAvV6PxsbGhMtFUUQoFJKHtbpcLjidToyMjAAY7Y9MHtbK/sjxxWIxPjY5xLCYH0r2irrdbixcuFCRbdPkMSyqiNJfPiaTqejC4mRmCQ0EAgnhYdmyZaqpwhbDbKjZeu1KQ00DgQBaWlqwbt26vFUJ8rG8CxUfQRBgNpthNpvHzEAYi8US1o/s7u6G3+9HOByGTqdLmKmV/ZGjWFnMLWkJGsqtSCSi2HtdiWGoNHXF/YmuQkqedTcajQiFQopsu1BNFKJEUcTAwADsdjvC4bBql0TQemVxusNQpWqx3W6HxWLB7NmzUVVVlffqgDQBUzEdCLGyWFikCXNKSkrGHLxFo1F52Y9U/ZHJ60daLBbVfXZOhSiKRXE/CwUri/mh1EyowGhlkWGxcDAsksxoNGJ4eDjfu5FT44XFUCiEjo4OdHZ2oqqqCvPnz1f1ejxaD4tTvX8jIyOw2+3o6elBQ0NDXoaapsPKIhUyvV6PsrIylJWVjflZOByWg+TQ0BC6u7sRCAQgiiLMZvOYiqSW+iNZWcwtzoaaH0pWFt1uN+rq6hTZNk0e310qo3RlsRiHocbf58HBQdjtdni9XjQ1NeHoo49W7MxZLnHpjETSUFO/3w+bzVYQy5ukks2Je9RyIM7KojYYjUYYjcYxJ9ni+yP9fj8GBgbgdDoRDAYhCMKY/khp/Ug1YVjMLYbF/FCysshhqIWF7y6SFWNYNBqN8Pv96OjogMPhgNlshs1mQ01NjWoOrjOh1+s13bOYSWWxUIeapiMNQy0mDIvaNlF/ZPz6kan6I+N7I61Wa0Ge5GFYzK1oNMp1bvNAycpiIBBIOaMz5QfDosooeWBbbGHR7/ejq6sLAwMDmD17dsENQcwmrQ9DTVeBGxkZgcPhQHd3d95mNZ2qbA5DVdOsqgyLxSk+ECZL7o/s7+9HIBBANBqF0WgcM6w1n/2RDIu5xQlu8iMcDiuyVJj0+a+W76tiwLBIsmIIi6Iooq+vD3a7HaIoora2Fnq9HvPnz8/3rilK6x+6qcLw4OAgDh8+jOHhYXlWU7UdUGSrsigIgmpeA2rZT8qtifojpRA5ODiYsj8y/o/JZFL0dcawmFschpofkUgk5Ymd6WJYLDx8d6mMkm8eLVefQqEQnE4nurq6UF1djUWLFqGsrAzDw8PYvyoam9MAACAASURBVH9/vnePpkmqLMZiMfT09MBut8tDiqurq1X7pZPNnkW14DBUmiyj0YjKykpUVlYmXC6KorzsRyAQQH9/P/x+P0ZGRiAIglyJjK9IZqMHi2Extzgban4o1bPo9XpVPaGgFjEskkytB9TjEUURHo8Hdrsdfr8fzc3NWLNmTcIZSKPRqOlevmIRjUbh9XrxxhtvYMaMGapaAzMdzoZKNHXShDmphp3H90dKLQl+v18e0hgfIKVAmWkgKbblbvKNYTE/lOpZHBgYGNPPTPnFsKgyuQh0auptSiUSiaCrqwtOpxNWqxU2m23ciUySZ0PVOrU/t8mkoaY+nw+CIKhyqGk6nOCGSBnp+iMjkYjcHzk8PCxXJGOxmNwfGR8ik/sjuc5ibjEs5odSlUW3242ampqsb5emjmGREkhDUdU4/t/n88HhcMDlcqGxsRErV66ccIa0YqrcSPdV7WExfqipyWTC7NmzUVlZiZ07d2rugKGYXp/xivE+5wIf18wYDAaUl5ejvLw84XJRFBPWj/R4POjs7EQwGIQoivKyH8PDw6ioqMDIyIji/ZHECW7yRcnKIpfNKCzqSwRFTukvHWmSG7WExVgsht7eXjgcDgiCAJvNhkWLFvHLOQVp+QwlZi/LhVAoJM9qWldXN2aoqRYPhIu1Z5GoEAmCAJPJBJPJlLY/0ufzwev1Yt++fWP6I+P/qOV7ttCxRzQ/lKqgc43FwsNPKgIGnRBcByDOWATjv4ZlFnq/VzAYhNPplINDa2sr1+SZgMFgUOUERkNDQ/JQ0+bmZqxdu7ZoziIX6zDUYrvPuaKFkQWFKr4/0uVyoaamRh5KF4vF5GpkIBCAx+NJ6I9MHtY6mf5IGsXXtXZwGGrhYVhUGSU+EHX7/wzjX24GALQbyxGtPRKGmW2I1S2CWLcQ4oyFgHUGkOcPY1EU4XK54HA4EAwG0dzcnJUeNengVOtnJqXKohpIFWO73Q6j0QibzYaampqiOyAo1mGopAyGxdxI/j7R6XQoLS1NeUIzvj/S5/Oht7cXgUAAsVgMJpMp5fqRfA4p35T8XnK73Zg3b55i26fJY1hUoWxPABFrOxehuiOh6/sHvAffQcnwYeg+fhr64MPy74gltRBnLIQ4YzFiMxZBnLEIYt1iwKL89MaRSAQdHR3o6OhAeXk55s6dO2YI0HQYDAZVD8/MlBqWRolf4qSurg5LlixRZB0ntSjGKhsnuCG1m8zJx4n6I6XZWt1ut9wfCSDl+pFGo5FBknJCyUmFXC4X6urqFNk2TQ3DIgEl1RDnHI/onOMx0Hg6RFGEraUFGO6F0LcPuv5/QOj/B4S+j6H78DHoQz75qmJF02gFsn4xxBmLIda3QqxdAOinH7y8Xi/sdjs8Hg9mzZqFVatWKRLoGBbzb2hoCHa7HUNDQ2hpaRmzxEmxKsaeRUCb/aeFgJXF3MjGSJX4/siqqqqEn4miKC/7EQgE0NvbC7/fj1AoBJ1Ol3L9SK1+nsZiMb6m80CpmVAB9iwWIm1+emickmfejUYjhoeHR4ecljVALGtAdO6Gz35BFIEhJ3R9+yD0ffyvP/ugO/wahGho9Fd0Boi1Cz4Lj/VtiNW3AmWNEw5ljcVi6O7uhsPhgNFoREtLC1pbWxX9MpDCotYVWs9i/FBTg8GA2bNno62tbVrPtdYOhotxGKqWnj8qTkq3NUgT5qSaWyAajSasH+l2u+H3++VZzlOtH6nmFgwum5EfSk6E6Ha7WVksMAyLlECaDXVcggBUtiBW2QLMP+Wzy6NhCO6DEHo/htC3F0LvXuicOyHs/R/5V0RLNcSGNsTq2yDWt0FsaINYtxDQmxAIBOBwONDb24v6+vqcLqpeLGGxUHoW44ea1tbWZm2oqVaWBoknCEJBBfxc4DBU5Wjt/VGo8lnt0uv1afsjpRDp9XpT9kcmrx9Z6K8XtS71pXaRSESxyqLH4+EENwWG7zAVUvLDe8KwOB69cXQynLqFAM7+7PKAB0L/Pgi9H0HXuxdCz0fQv/8whEgAwGgV0m9twUjZHMxqXokj568DGuuBHM7GajQaCyJEKS3fw1C9Xi8OHz6MoaEhNDc3Z32oqU6nQzQaVfVZ8mQ6na4oXpvxGBaVw7CYG6IoFmS1y2AwoKKiAhUViXMNiKKIUCgkD2t1uVzw+/0YGRkBAHn9yPiqZKH0R7KymB9KVhaLoS1IbRgWKYHJZJpaWBxPSRXElrUQW9ZC6rwKBQPo+8db8B/cibpIF6pDHah37YXw978Cfx/9HbGyBbGGJRAblkJsWIZY49KMhrFOheFfy4VoncFgQCgUyultiqIoDzXV6XRZGWo6Hr1er7n+vmz2LBbCgR1RMYhGo6p6vwmCALPZDLPZjOrq6oSfxWIxef1Iv9+Pnp4e+P1+hMPhhP7I+IpkLit9DIv5oVRlkScKCxPDogoVZGUxA4ODg7Db7fB6vWhqmoc5Zx4nf9iEAGC4D0LPHuh6PoTQswdCz4fQ/fPPEDD64SFa6yA2LEGscTnExmWINS4DKm3TDpAchpp94XAYTqcTnZ2dqKmpQVtbm+KzmkqVRS3hbKiUTaws5oZSi5XngxQIS0pKxkw6Eo1G5WU//H6/XJGUhoamWj8y248Lw2J+hMNhRb7TpbVH+TlVWBgWKUG2D7ij0ag8YY3ZbE6/Xl7pDIjzTkR03omfXTbig9D3EYTuPdD17IbQvRv6t++DEBsNPaKlGmLjUsQal0FsXD4aIKvmTCpAGgwGebiNluViGKo0g+3g4KAiQ03T0eLModmc4IZBgQBWmHOhGNbtBUa/U8rKylBWVjbmZ+FwWA6SQ0ND6O7uRiAQgCiK8rIf8VVJs9k8pdemFC4otyKRiCLf7W63e8zsv5R/DIsqpOSXfba27ff7Ybfb0d/fj8bGRrS3t8NisUx+Q+YyiM1rIDavkYexIhIcnUin+4PRKmT3B9Dv/AWE2GhFVLRUjQbHme0QZy5HrLEdqGgaN0AWS2VRqdlQRVFEX18fDh8+LA81VXoG21Ty3ZOpBFYWKZv4uOZOsYdyo9EIo9GYtj/S7/djYGAATqcTwWAQgiDI/ZHJ60eOhxPc5IdSS2dw2YzCxHdYEYvGRPhDUQyPRDD8r79D0Rh6/TGEIlGYDJM7WyeFBrvdDlEU0dLSgiOPPHJaZ1hDkRi6h4Lo8ATRNRhEpyeIjsEAugZFeIOtWFC/Gq2Ly9G2wYxWQwdKB/ZA1/0BhK5diRVIa91oeGxcDnHWSsRmrQCso1MzZzL0VhRF9AyN4GD/MGbXWtFUlbsJeLIl28NQk4eatra2ppyBL1e0WlnM5n1SQ3WRYVE5anj+Sdsm6o+MXz+yu7s7oT8yeVir1WrlMNQ8UaqyODAwwJlQCxDDogpN9sv+92878NxHPXIglP4OhMc/CL3pb39FY4UFzdUWNFWVoLmqBE3VltG/q0rQUGGGXje6HyMjI+jo6EBXVxdqamqwaNGilMNSxiOKIpyeIP7R48U/un040DeMjn+Fwn5fCMnHjTPKTWiqLEGFxYDXPhnA/+7qkn82p3Y+FjeuQOuCcixfb8ZKcwfMfR9A1zUaIHUHX4Igjt5vsdKG2KwVKKttQ0m4FgjNBUylCEViONA3jH09Xuzr9mFftxf7enzw+MNxt2PFMfNqcOwRNVgztwbllsJ/K2Wr8ubz+XD48GEMDg6iqakpp0NN09FiZTFbw1AFQWAII6KCFh8IkyX3R/b39yMQCCAQCMBgMMDn8yUMa7VYLEUxFDhfWFksLvk/wiPFRUURggA0lJtRWmdFqcmAUrMeVpNe/nep2YBSkx5GvQ5vf/hPwFqNbl8EHZ4g3jjoQq93JCG0GXQCGsqNqDGJqDCKmFFVhhnVM1AWNcI66EKJcfBft2GA1aRHiXH09qwmPbqHgtjX7cM/enyjAbHHh+GRzw7ym6tL0Fxlwfr5tWiqLMHMKgtmVVrQVGVBY4UFJkPiF0CvdwR7u7zY2zWEvV1e7O4YxHMf9QAAjHoBK1rasW7eiVi3vAbVhhDQtRuGnvdh7duNikPvoPTj7WgFEHv7Bnyqs+Gd8Dy8G5uP92Pz0WFoxoL6Cpy6uB6LGsowb0Yp/tHjwxsHBvDUB1149B0n9DoBy5oqsG5eDdbOrUZ7cyXMxsI70zmdYajJQ01tNltehpqmo8XKIoehUjaxskhqNV5/5KeffioPXfX7/RgcHEzZHxn/x2Qy8X0wTUpVdD0eD8NiAWJYVKHJfshdutaGS9faMv79qmA5bLZZCb0GoUgMnYNB2Ad8+OhwDz7pdMEVEjAUMeKAL4IPXT4MhwYRjWV+kFduMWBhQxnOXj4TCxvKsLChHAvqS1FqntzLsr7cjPpyM044sk6+zOMP4wPnIN486MKbn7rw85cO4ucvHYy71op//QHqMIhlugM4xnIYa0wH8UXhHVwQfQkA8P/Ze/P4uO763vt9zpkzi0a7RrKsXbZl2fIS27Ed21ntJHY2AiFQCKVh7W0ptClPaVn6cJ8LveU+vYUWuNBCgEKgCYEQIDQJIRsJ2WPHcRzHW2Jr36UZSaPZ55xz/5BnMlo9kueMZvm9X695yRrJR2dmzvL9/D7fxbAWYRRtRS/ZjlG+Db36YnavauDDuxsIR3WO9Izz3JlRnj/j5jt/aOffnm7HZpHZ1lDK7uYydq0qZ8PKIizK8q9wLiUNNRKJ0NvbS29vL2VlZcuearoQuTo640KFU2x8SU9PDxaLBafTKVbf8xQhFgW5hqZp2Gw2SkpKKCkpmfYzwzDiYz8CgQAjIyPx+ZGSJMWdyJnzIwXJYca1xO12U19fn/LtCi4MIRazFDNX3+eq4QsH/QSGulHcbg6sXslHr1iLzWab9juGYRDRpuogpx7RqZrIsEYgcu65kIaryErrikJqSuymBS6lBSpXrnVx5TkB6faFOdQ5RjCq4bRaKExwUwttFo4dOcTey//u3AvRCbvPIPW+gtz3ClLfYZQXvoFkTLlyelkzRu0O5NrtXFK7nZ171/Ppq9fgDUY52OnhhbNuXmz38C9PnIEnzqDIEhVOK5VFVqoKbVQW2agstE59LbJSWWijstCGq9A6yzVNJYtx3iYnJ+nq6sLj8WRUqulCiNEZ04lGo/T29tLT00N5eTmrVq0iGo0SCASYmJigv7+fYDCIYRjTmkrExORyBU3CWRQIBMmyUO1crGHOXM31Eusj/X4//f39+P3+eHfVueZHitpI83G73WzZsmW5d0Mwg8yO/gTLgqqqhMNhdF1naGiI7u5uJEmioaGBdevWzSvwJEnCapGwWmRKCzJrda7caWV/W9W8P7cpCa9JkjEqWjAqWtA3v3/qubAPaeAoct8hpN5DyGefRDn2cwAMqxNj5TZKa7dzTe0O9l21Ha5vZXQyzEsdbk4NTDI0GWLYG6Z/IsjR3gnc/tm1mDAlcutKHWytL2FHUykXN5TiKrTN/sUlcD5hbhgGIyMjdHZ2AtDY2Mj69euzxonIRbG4lNTaQCAQ70RcU1PDzp074+e0YRhzrr4nBk0DAwP4fL540DQzhcuMWWmJCLFoHsJZNB9x7KaXpaZDLlQfGVtU8/v9+Hy+uCOp6zqqqs66HuZbhoau66ZdR0TNYmYixGKWYnZA1dfXx9mzZ6moqEjLQPWMx+rEaNiN1rB76nvDgLFO5N5DyL0HkXoPobzwzbfdR9c6VtTt4Ka6ndxw8U4obZs2uiOq6Yz6wgxPhhn2TgnJKUEZon3Uz32He/nJS93AVDOd7Y2l7Ggs5eLGMupKU+vIRqPReFfT0tLSRTcoyhQURTlvV9tsYzFpqOPj43R0dBAIBGhsbKSlpSWpACaWjjXX0O1oNBoXkV6vl8HBwXgt0Fwt7q1W65Jep0CQKwhBnl7MqJ2zWCwUFRVRVFQ07XnDMKbNjxwbG6Ovr29WhkaiK5mL9ZFmdUKFqTmLLpfr/L8oSCtCLAqAqYug2+2mu7sbr9dLYWEhu3btyqu0i0Xd5CUJyprQy5rQN75n6rnwJFLfq8g9L089Tvwa5chPprbtrESv2zk1L7J+F5YVG1lRbGdF8dyzJ8NRnTf6JzjUOcYrnWM8enyIXxzuA2BFsY0djWVcu76Sq9a6sC+xmc7MVNMdO3Zkdb2GoiiEQqHl3o2Ucr401Fg9YmdnJ6qq0tTURGlpacqCE4vFQnFx8Zyz0hLdyMHBwXiL+wt1I4WzaB5CyJiPrut55TItN+kcnSFJElarFavVumB9pN/vZ3h4mEAgMKs+MvGamK33W7M6ocKUWBSjMzIPIRazlFTd8CORCH19ffT29lJUVERzczPRaJTh4eG8EooWi4VoNHphF0BrIUbT5WhNl6MB6BrSyEmknoNxASmdeggAQy3AqN2OXr8LvX4XRs02UN92b60Wma31pWytL+VPLwNdN3hz2MehTg+HOsd44aybB18foMCqcM26Sm7cVM2eVeXnrXmMiYvYLMxsSzVdiFxNQ51LOM2sR9y4ceN53f9UirDzuZGBQACfz5eUG6mq6rTjLxeOxUxFiEXzEWIxvWTKnMXE+siZYkfX9bgbGQgEGBsbm1YfOVNEZnp9pJnO4sTEBKWlpaZsW7B0hFjMU7xeL11dXYyNjVFTU8P27dvjKWRerzfn0vnOR6ypT0pXy2QFo2oDRtUG9G0fnnrO24/c/RJy94tIPS+iPPPPWDAwZAtG9UVTwrFhD3rdTrC/vXIpy9K5jrGF/PHOejTd4OUODw+9PsCjJ4b4zdEBShwW9q+v4sZN1exsKovPwYS3xYXf72doaChrU00XIhdHZ8x8TfPVI2YSC6VwxVbefT7fLDcytvIuSVK8ZloE3alHiEVzEcdtesmG91uWZZxO55ydxBPrIycnJxkaGiIQCKDrOlardVZaq91uXmPAZDHLWYwtZmb655mPCLGYpSzlYqHrOgMDA3R3d6Oq6ryz8ubqhprrxJxF0ylaid72LvS2d019HxxH7jmI1PMicveLKAfvRHrp2xhIGCs2otfvxmjYjV6/CwrednAUWWL3qnJ2ryrnv9+4jufPunno9QEeOjbIfYf7qCmx855tNdy4royAZwC3201NTQ0lJSW0tLTM6mSbCyiKknPOYiwNdan1iJnEQivvmqbF07c8Hg9er5dXXnll1py0xE6tyx0wZSMivdd8skG8CDKH89VHJl4XY/WRwKz5kQ6HI231kZFIxNTu6OLannkIsZgHBAIBuru7GRoaoqqqis2bN+NwOOb9/VjnxHwibWJxJvYS9DXXwJprplJXIwGkvleQu15A7n4B5ciPkQ7dCUw1zTEa9qA3XoresBsKporArRaZq9a6uGqti2BE48mTw9z9Ugff/P1ZvvUUXNpUzO17WmlsrGBsbCznBFWMXHMWYynDk5OTnD17NuX1iJmEoijxgKmgoADDMFi/fv2sOqChoSF8Ph+RSGRaN8OYkDS7U2sukIvHTyYhxGJ6ydXjObE+cmZaZmLNeCAQYGhoCL/fTzgcRpKkWW5kQUFBSsXdBZfszEMgEFgwNhUsH0IsZinJjkHo7u4mEolQX1/PmjVrkrqJ5eJw8/OxbGJxJqoDo/EytMbLpsSjFkbqfxW560XkrueQX78X5fB/AKBXrp8Sjw170Bt2E7WWMtjXS6m3ly/sLkHav5qHTo7xyyN9/OndR6gttXNdk0pTc4RcbG6bK87izHpEh8PB1q1bl3u30kZibWWybqTP54s3lNB1fdaqu9PpFG4kwllMB2aOFRBMxzCMvDymE2vGZ6Jp2rTmYx6PB7/fH6/tTMUopEgkMufsygtldHSUsrKylG9XcOEIsZhjhMNhent742MQWlpaZqU3CGaTMWJxJooVo+4StLpL0PbcAVoEaeA15K7nkTufRT76U5RXfgBAxNmIq3YXdesPoKzaAPYS2hoquWPfah4/OczdL3fzgyNjPNpxlM9d18rV6ypzKqjJdmdxvnrE559/frl3La0k24gn0Y1MxDAMwuEwPp8v3pWws7OTcDg8y43Mt2HbosGN+RiGkTfH03JjGIZwcWegKMqC9ZGJo5Dmqo9MdCXnq480y1l0u92iE2qGIsRiljLzBB4fH6erqwuv10ttbW1KGl/kU2CRNXWaiopRu51ozcWMtnyArvYzFIydotHoomj0CM6zDyCd/hmGJE81zGm8DFvjZdzQegnXb7iYu3//Gj856uWT9x5lR2Mpnz2wlk21xef/u1lAtjriuVCPmElIkoTNZsNms83pRsY6tZ7PjczVGWm59noyDU3TxHucJjKlE2q2sNAopHA4HE9r9Xg89Pb2xusjYy5m7LoYCoVMed/dbves7tqCzECIxSxG0zT6+/vp6enBbrdTX19PeXl5Sm5UsZQ+M4uYMwmLxZIVM/qi0Sh9fX309PRQXFxMy7o2iooumfoZQDQ0VfPY8Qxy57MoL/87lhf/D4asYtTt4B3FG7lu7+U8HmzlG0938p47X+Ydm6u5Y99q6suyu1Ygm0ZnxOoROzo6sFqtaalHzJYA1sw5i4qiUFhYOKsTcGKwFBORsRogWZbjgVKswU62upH5mLKXboTblT7MHOGQTyQusM1MA9V1fVrd+ODgIGNjYxw/fnxaF+tEV3Kpn4nb7cblcqXiJQlSjDjLspiDBw/icrnYsmVLyvPHrVar6R2vMomMTUM9h9/vp6uri9HRUVauXDlt1Mk0LDaMhj1oDXvQ+CyEJ5F6Xj4nHp+h8tj3kI7dye22Im5r3M3T0Q38y/E69r/ez5Utldy2o47L1lRMG7uRLWSDszizHnHTpk3nnY8oMJ+FgqWYGzlXbWRi6lZMSGayG5lP2SLLhWhwkz6Es2g+scWyxJm6Xq83Xkcfuzb6/X7cbne8PtJiscxKaz1ffaTH4xE1ixlKfiiBHESSJHbt2mXa9mNpmfnSmSoTxaJhGLjdbjo7O4lGozQ0NLB27drFBSLWQoxV+9BW7UMDet88imPgEFW+46jtf+DasUe51gJeRyVPdW/kwbc28I2ii9m/vY33bKvBVZg9IzZiYyYykUyZj5gNYsFMZ3EpJONG+v1+RkZG8Pv9hEKhaW5kYqdWEdjmPkIspg8hFpcHXdfj7/tc10aYaoITE5Jer5fBwUECgUB8HFLsenj8+HHa2tpoamrC7XazYcOGdL8cQRIIsZjFmBlU5dv4jEwSi7NSTVPYpEhyuhiv20t580ennhjrRO54hoKOp7mp/Q+8w/g9hODYM008+IfNBOouZ9tl+9m5ujorREamIeoRF0+micX5SNaN9Pv9jI6O4vf7Z7mRMSGZLjcyGxYLsh0hFtOHEIuZi6qqqKq6YH1kf38/jzzyCP/+7//O4OAg4XCYhoYGXn/9ddauXRt/LLWO8aMf/SgPPvggVVVVHDt2LBUvK28RYjGLMVssZkXDlxShquqyi8WkU00vAIvFgs/ne/uJ0kb0LY3oWz4IuoY0+Dpy+1M0n36C9QMPo/T/hsDP/54jlo1M1lxOyaYDrGvbilUVN+j5mKseUaTW5BcLuZGRSCTeqXV0dJTu7u453cjYI9XBsBCL5iLEYvoQYjH9XGjMOXOR7dvf/nb8Z3/6p3/KbbfdhtVq5fTp0/znf/4np0+fZmRkBLvdzj/+4z+yb9++pP/Whz/8YT71qU9x++23X9A+C4RYFMxDvolFi8WyLK83Jammi2DBWYSygrFyC9rKLVj2/DXR8CTBs8/Re/hh6nv+QG33N6D7G/Q8VMmpwh1EmvZSu+VaWupXigCUKUe4p6eH3t7elNcj5pMjlC3O4lJIHLQ9VyOJWKfWmW6kqqrxmsjYw2azLfqYyNX3NZPQdT1vav2XG9HgJv2YKdDHx8fZunUrDQ0NXH/99dN+5vf7F339uuKKK+jo6EjhHuYv4izLYswMHlVVne5A5TjpntGnaVo81bSwsJA1a9bMStcwA4vFknzHUGshlnUHaFx3AAD34Fn6Dj+MfPb37Jr4Pc43HiZyTOGo1Mpg1WWs2fNOGtdthzwRNTHMrkeUZTklYjFbxGa27GeqkWV5zvloMTcy1mAn0Y2MDeeeKSTnC+byadFhudB1XbzHaUI4i+nHrBmLsPDoDNEIbnkRYlEwJ/nmLKbr5p4oLKqrq7n44otTnmq6EAs6i+fBuWIVLdd/CvgUaBH6Tz+P++hvqer9AxcP3Qm/vpNRuQJf/ZWs2HoTrLoSbKmptcxExsfHaW9vJxgMmlqPGFvIyKfUNuGAvU2iG1laWjrtZzE3MlFIBgIBNE1DVdVZnVrF+2o+ic0/BOYSO84F6cPMLvmhUEiIwgxFiMUsxkyBExudIbhwDMPA4/HQ2dlJOBxe1kYniqKkpjZTUSlffyXl668EYHi4h6NP/wrpzONs73gEW+cv0SQFvXYnUsu16Gv2Y1S0mO46xjqimvXeLkc9YiZ3eTWDXE5DTTWJbmRlZWX8+UQ3MtbSvqenh8nJSQzDYHJyclanVpHOlxqEs5g+hLOYfsxyFsU1P7MRdwfBnORbN9QYqUzT0jSN/v5+uru7KSwsZNWqVZSUlKRk20vlQpzFhSiurOOy9/wlUe2TPH68j4PPPkbNyHPs6z7Cup4vw++/zKi6kpNFu3iz5FJ6irdiWOzYLDKXNJexs7EMOQWzHc1y4cysRzwfsTRUgSBZ5nMjBwYGCIVCuFyuuJD0eDzx2WiJbmTsYbfbhfhZBIZh5FUWwHIixGL6iUQipojF2IKouNZkJkIsZjFm1yzmm7MYG59xoRfCmamm27Ztw2bLjHmFZo8IsSgy122q47pNH+FY361858Vu+rreYkfkELuih9jhfohL3b/Cb9h43tjIE9pWPvP0VuTiam7cuIJ3bK5mfXXRko9tRVFS6sJlwnzEdNfTLjfCWTQXSZLmrI0Eps2N9Hg89Pb2EgwG47WRM4WkcCNnk28p48uJaHCTfsx6zycmJlLet+G2227jqaeeYmRkhLq6Or70sqS8kAAAIABJREFUpS/xsY99LKV/I18QZ5lgTlIddGcDFyIWZ6aaNjQ0ZORMvXS6VBtrivmnd28ANgDvnHoyEiDS+Ry2M49x9ZnHuWb8+/wvFc7SygMvb+bvX9hKqKKNmzZX845N1dSXL869k2U5Jc5puuoRk0GkoQpSxfkyJxaqjQwGg/FOrYlupMVimdVgJ5/dSCEW04dwFtNPJBLBbrenfLsLNbdZKj/96U9Tur18RojFLCZfb8ZmsRTXLTHV1Ol0ZkSqaUajOtDXXIO+5howDKThE8hvPUrTm7/jr/t+wact9zHsr+S3f9jCPzy1jfEVu9i/qY7rN6ygpvT8N6gLceEydT6iSEMVpIqlptnLshwXgjNJ7NQ604202+2zhGSuO0FCLKYPIRbTj1nOotvtpry8POXbFaSG3L5qCy6YfGq1rqpq0mIxGAzS1dXF8PAwK1asyKhU06xBkjCq2tCq2tD2/DX4hpDfepzyNx/hg+1Pc3v0MfweB0/+/iL+9fGLGa2+gis2r+b6DVWsKJ5bOC6lJnM56xGTIVXOYracx8JZzC5UVaWkpGTWIlnMjZyrNtJisUzr0ppLbqQQi+lDiMX0Y1bN4ujoaMqdRUHqEGIxizH7xhoLvHN9JTiGxWJZsE7TMAzGxsbo7OwkFApRX1/PmjVrRGCQKpxV6Bd9AP2iD0AkgNz5LLY3H+G6U7/lpsCLRN3f4cUn1vGDx7YzUL2XnRdt4kBbFZVFb4v0xTiLgUCAzs5ORkdHl60eMRmEsyhIFelc/EvGjfT7/YyNjdHX10cwGATAbrfPGvmRTfcgIRbThxCL6ccsZ9Hj8QixmMFkzxVYMCdmrsLHxmdk0436QpgvDVXTNAYGBujq6sLpdNLU1DSrpifbyHjHWHWgr7kWfc21cN0/o/e+gvzmI+w4+TCXjd0Fo3fx+uNN/OzRHbxVfiUj9mZUi0Io4KfA4cfpsFFdbOeqtS62N5aiKm8Hb2NjY3R0dBAKhWhsbGTt2rUZHdyJBjeCXCNZN7Kvrw+/3x8PUGc22HE4HBl3HRNiMb1k2uef65jlLLrdblwuV8q3axa/+tWv+NKXvjTtuaNHj/LQQw9x/fXXL9NemUd+qADBkoiNz3A4HMu9K2lhpljM1VTTrHOMJRmjbgda3Q7Y+0XCo28hv/lbVh97kL8Zvg8m7qPPV8uL1l08qV/MydBatIkIT54a4UcvdFFkt3DFmgourlapkcYoddoyph4xGfKxwY3AHDJ9rEOybuT4+Dj9/f1zupGxx3JlCYg5i+lDLCqlHzOdxbVr16Z8u2Zxyy23cMstt8S/v/POO7n77rs5cODAMu6VeWRJtCiYDzNX4fNtfIbFYonX1nR2dhIMBmloaMi5VNOYKM4asTgDo2INWsVfouz6S0LeAeQ3f0v1qYe4pesB3q3fT7SgCmntTfhWXc9TgRb+67U+nj41yEPHwCJL7GyysjfkZW+rnfqyzF8IyTdnUWAeGZ9RsADzuZGGYRAIBOJCsr+/P+5GKooyZ6dWM6/nmS7IBYILwaxrSLY5i4mcPn2aL3/5yzz//PM5e+5nZ7QoSAv5JBZ1XY+vVk9OTuZEqul8LKUJTMZSVI2+7SPo2z4CgTFGX7ibkv5nKDh6D8WH/4Pr1GKuqN+L+t73ctS2lSdOj/HkqWH+8ben+cffnmZtlZO9rZXsbXWxubYERc68QDqVC0LZKhQEgvmQJGleNzIajcY7tSa6kYZhzNmpNRVupEhDTQ/ZvPAhmI0ZozPSQSQS4QMf+ABf/epXaWhoWO7dMQ0hFrMcMy+W+SAWg8Eg3d3dDA4OUlJSQkVFBZs3b17u3TIVi8WSO2IxEUcpI7XXcNqxDUvzJ2iVOykbeJaSM48hnX2AXfYSdq45wGevewftJTt58q0Jnjw1wvef6+S7z3RQ7lS5qsXF3tZKLl1djtOWGZdH4SwKUkW+BdgWi4Xi4uJZw74Nw5hWGzkwMIDP54u7kXN1al2MAMyn93i5EKI8/Zh5/RgbG8tKsfjFL36RDRs28P73v3+5d8VUMiMaEmQkqqri8/mWezdMIdbVNBAIUF9fz549e/D7/Zw5c2a5d810cspZZOoGNjg4SGdnJ5qmUVZWxvr16wHQuB0tGkRufwr55IPIb/0O5djPabEVsXrNAT522c14qi/lmQ4fvz81zOMnh/nlkX6sFplLV5ezf30Ve1tdlBVYl+31iW6oAkFqkSQJh8OBw+GYFaDG3Ei/38/ExAQDAwMEAoG4GzmzU2smdlDOB0Qn1PRjZvnK2NhY1s1ZfOqpp7j//vs5fPjwcu+K6QixmOUIZzF5dF2PdzW12+00NjZSWloafw/n64aaayiKkhOvc675iGNjY4RCoem/aLGjt1yH3nIdaGHkjmeQT/4G+fRvUd74BZXWQt7VcoCbN99M6B1XcrgvyOMnh3n8xDC/PzWCIkvsaCxl//oqrllfOe+MR7PItwY3AvPIN2dxKSzGjfT7/UQikbgbWVBQQDQaxefz4XA4hPNlItlcd5+tmNUJ1TAMNE3LqoUXj8fDRz7yEe655x6KioqWe3dMR5xpgnmxWq2Ew+Hl3o0LJhQK0dXVxeDgICtWrGDLli3Y7bMD/nwSi9nsLCbOR6ytreWSSy6JBw1er3fh16ZY0Vdfjb76arjun5E6nkU5+Rvk0w+jvHE/FlsRl7Zcx+71t/CFay/njaEQjx0f4ncnhvjyw6f48sOnuKiumL1rK9nRVMbm2mKsFnMDwlQ5i0IkCIRYXDrJupGaptHe3j6nGxl7WK3Ll6mQKwhnMf1Eo1FTBV02XZu+853vMDQ0xCc+8Ylpz3/+85/nfe973zLtlXkIsZjlCGdxfmKppn6/n4aGBnbv3r3gzSXbRVSyZKsoTmY+4qLq+xQrxup9RFfvmxKOnc+gnPgN8umHUI7dh8VeypbWG9m0/p18et9lnBkN8ejxIR47OcTXn5xKV7ZZZLbUl7CzsYztTaVsqSvBrqY2gBE1iwJBZpPoRnZ3d7Nx40Zgths5ODg4pxuZODdSuJHJIcRi+jFr7nY2zvP+/Oc/z+c///nl3o20kV2fjiCtZKNYPF+q6UJk06rWhZBNojixHtFms9HY2LjgfMQlvzZFxVi1j+iqfXDd/0Y++xTyiV8jn3gA5bW7MQpctLbexJq2W/jEFZfg9kd5pWuMlzs8HOzw8K2nz2I8BVaLzJ5V5VzdWslVrS6qii58LqdIQxWkCuEsppfzuZGBQACfz4fX62VwcHBBN1JVVfHZJSDEYvoxKw3V7XZnzdzjfEWIxSzHzJuHoihZE6SGQiG6u7sZGBigqqpq3lRTwdTnmunpxXPVI87VGn8mKXHhFCt6y370lv0QCSCffXJKOL7+M5RXf4RRVENl27vY3/Zurl23CSSJiUCEV7rGeO6MmydPDfPU6RH4L9hcW8zV6yrZ11pJS5VzSeeraHAjSBVCLJrLYs5Ti8VCUVHRrHonwzAIhUJxN3JoaAifz0ckEkGW5VkNdvLVjRRiMf2YVSearWMz8gkhFgVZzfj4OJ2dnfh8Purr68+bapoMuR5QZfLojIXqEZMh5a6p6kBvvRG99UYITyK/+Tvk479COXgnlpf+Db18NXrbLZS0vZu9rWvY21rJ31+/ltNDPp48OcyTp4b51yfO8K9PnKGuzMG+Vhf7WivZ3liKqiQX4AlnUSDIDlJx75AkCbvdjt1un9UdUtO0uIicnJxkaGiIQCCAruvYbLZpTqTT6cxpN1I0uEk/kUiEwsLClG93dHQ06zqh5hviTMty0nEjyDTxpOs6g4ODdHV1YbVa46mJqdjHmNjI5ZtQJnZDTaYeMRlMre+zFqJvuBV9w63gdyOfehDl+K9Qnv0alme/il59EfqG96C1vYvWFStoXVHIJ65sZsgb4venhnni5DD3Hurlxy92U2y3cEWLi6vXubh8jYsi+/zHm6hZFKSKTLuW5xpmz/5TFCUpN3J4eJjOzk7C4fA0NzLxke1uZK7fpzMRswS6x+MRzmKGI860HECSJNPS1DJJPIVCIXp6eujv76eyspLNmzfjcDhS+jdidZqZ8HrNIlNqFhdbj5gMaUudLihH33o7+tbbwduPcvxXyG/cj+WJL6I8+f9hNF6OtuFW9NabqCoq5H3b63jf9jr8YY3nz4zyxKmpsRwPvj6ARZbY2VQ25Tquq6S2dPoxLdJQBYLsYLkGxSfrRvp8PoaHh+d1I2OdWrNhQUHTNGy2C68JFySPWTWLHo9HOIsZTu5GxIKUEBufsZziyYxU0/nI1k6hi2G5xeJS6xGTQZbl9L+2opVol/wF2iV/gTRyGvmN+1GO34/60F9h/O7vpmY8bnwvevNVFFhVrllfxTXrq9B0gyM94/F01f/529P8z9+e5qN7Gvj01WviIzlEGqogVQhn0VyWSywuxEJuZDgcxufzxd1Iv98/rxvpcDgyqkZQ1CymHzNrFpubm1O+XUHqEGIxBzDTWVyujqhmppouRD6IxeV6jRdaj5gMy92UyXCtRbvy82hXfA6p9yDKG/dPdVQ98WuMAhda27vRN74Xo3oziixxcUMpFzeU8rf7W2gf8fHDF7r4j+e7eKndw9fes5Fml1M4i4KUIcSiuWSiWJwPSZKw2WzYbLY53chAIJDRbqQQi+nHzG6o27dvT/l2BalDiEXBgqRbLIbD4XhXU5fLZUqq6ULkg1hMt7OYqnrEZFgWZ3EuJAmjbifRup1wzT8gn3kC+dh9KK/+CMuhO9Er1qJvfC/axvdAcS0AzS4nX37Heq5YU8HfP3CCd3/3Zf7fG1q5urlAOIsCQRaQTWJxIRRFobCwcFYzk5gbGUtrHRkZwe/3EwqFkGUZh8Mxq1OrWYJONLhJP5qmmXJ8i5rFzEecaTmAmSt66RKLExMTdHZ24vV6qa+vZ9euXcuyapiNsyUXSzrEohn1iMmQka6JYkVfez362ushMIZ88gGUY/dhefofUZ7+CkbTZWgb3zfVcdXq5Jr1VWysKeZvf/kGX/j1ca5tLeeDrWIFXXDhCGfRXHJFLM5Hohs583qe6EYmCkld17FarbM6tV6oGymcxeXBjOuHx+PB5XKlfLuC1CHEomBBzBRPuq4zNDREV1cXFouFxsZGysvLlzWYyQdn0cy0xsR6xIqKipTWI+YEjlL0rR9C3/oh8LSjHLsP5djPUR/8FMajn0VfdzPapvdRXb+LH31oG99/toNvPHmGg50yHw90cNv2OgoX6JwqEJwPIRbNI9fF4kIk60aOjo7S3d09y41MfCQjAoVYzB3EnMXMR0QdOYDZzqLP50vpNsPhcLyraUVFBRs3bswYQWGxWAgEAsu9G1lHOuoRc46yZrTL/w7tss8gdb+E8vq9yCd/g3L0pxglDWib/og/2/x+ttZs4p9/d5KvPvYW332mgw/sqOP2XfW4CkUnQMHiELWv5qLruhDjM1jIjdR1PS4iY0JyPjeyoKAAm80Wf3+FWEwvZr7fk5OTsxowCTILEc0JFkRVVcLhcEq2NTExQVdXFxMTE9TV1WWkoMgHZzGVpLMeMWeRZIyG3UQbdsO1X0E+/TDK6/fG5zfuqt/D15oux/uOD/LdFwa589kOfvhCF7dureFjexqoL09uoSUUCtHf34/NZsPpdGK320Vgm2eINFRzMQxDXP8WgSzL87qRkUgk3qk10Y2UJImCggICgQDDw8Px+kghHM3FrBrR2AKWOG8ym8yK1AVLwsybv9VqvaA01LlSTTds2JCxAYsQi+dnueoR8wKrc2rMxsb3wng3yus/Qzl6Ly3d/4Rx6t/4t7Zb6P6jd/Ht02X84nAvPzvUww0bV/CxSxtpW1k85yYnJyfp6OjA6/VSWVnJ+Pg4/f39BINBABwORzzgcjqdGdciXyDIFvI5DTWVSJKE1WrFarXO6UYGAgHGx8cJBoO43W4CgQCapqGqavxaNpcbKVg6ZnVCNQxDLGJlAUIsChZkqTWLmZxquhCqquaFWIzN7ltMYJNN9Yg5cfMpqUe77DMEdnyKjqfupi18GPn1+2h69cf8k2sdX7jqj/i+9xJ+eGSEB18fZEdjKR/a3cC+1koUWcLj8dDe3o6maTQ3N9PW1kYkEpn2vsQCr1iL/MQ0sFiL/EQhaUawMB858RlmGOI9NRchFs1HluX4taipqSn+fMyNjKW0ut3uaW5kYm2kcCMXTyQSMcVZ9Pv9OJ3OlG9XkFqEWMwBMqkbqtfrpbOzM6NTTRfCYrHkfDdUeLsjajKBTbbVI8qyjK7rORMIyIoFT+lGopd8DPb//8gnfo3y2j2UPfdlPiOr/FXrfh6zH+CfTqt86t6jVBep7KuT2b+mkLaW1ZSUlABz16vFAi+n00llZWX8+ZkDuwcHB/H5fPFUpMSAq6CgQKS0ZglCLJqLEIvpY+b1LNGNLC0tnfazxEUxv9+Px+PB7/fH3ciZnVqFGzmbaDRqymLh6OjorDmfgswjcyM+QUaQzJBzwzDiqaayLGd8qulC5EsaqsViid8o5yNb6xFjx2zOiMXE7rW2IvQtf4K+5U+Qhk8gv3YP1mP3cVPgIQ4UrOBg7RV8N7iPe06U8OszUW4dGuCje2zUlNrj20tGMCw0sDtx9d7j8dDb20swGIzXEs0Ukks5ZiRJEsJGkHUIsZgeFnttSFwUm0lip9aZ17O5OrVm8kKpmZjlLIpOqNlBfh71OcZyBVSRSISenh76+vooLy+nra0t69MJ0j2wfrlQFGVOUZwL9YiyLJ9XCGcTsZThmRiV6wle+d/pbvgA0Td+Q7PnWXYP/oLd/IKJ1Vdwn3E1XzsU5r7DvfzFFc18ZE9jXIRdCKqqUlJSEncsY8RW730+Hz6fj+HhYQKBALquY7fbZwnJhT6fVOynYDZCgJuLrut5KybSSSo7c6bCjcyH7IpoNIrVak35dt1ut3AWswBxVcsRzA6uEoMMr9dLV1cX4+PjWZlquhC5fLFPZKYozqZ6xPMRS0PNFeY6JgOBAB0dHXg8Hurq6mi8+TMoymcJj3WhvHYPxUfv4eOTT/PhkkoeVa/hK09ewi+P9PP5/avY3WyO+J9v9d4wDEKhUDyldWBgYFpKa2JNZKwhhUCQjQhnMT2kY2zGQm5kLLvC5/PF3chQKASQs25kJBIxJSbweDzCWcwCsv8IFphOLDXT4/HQ2dkZTzVta2vLG3GVa8TEYrbVIyZDLrvDExMTtLe3EwwGaWxsZN26ddPPwdIGtCs/h3b5Z5DPPIF85Cdcf+Zn3GD7KQcDF/H9n+3ll2uu5YO7m9mwshBVMT+wlSQJu92O3W6fFRQkBl2JDSkCgQAnTpygsLBwWpdWEYhfGMJZNBchFtODWWMckmWh7IpgMDinG5m4MJaNbqRZNYvCWcwOsjsqFMQxy1mMRCKEw2FefPFFXC5XTqSaJkOuB1XRaJTTp08jSVJW1SMmQ645i4ZhEI1GOXToEJIk0dzcTFlZ2cLHp2xBbzmA3nIAJvpQjt7DxUfuZof+dYY6f8S9Z6/if8jXUl23ih2NpexsLGH9yiIscnqP+fmCrldeeYX6+vq4Izk8PIzf78cwDOx2+yw3MtsXONJFrl/Xlhtd18X7mwbS4SwuBVmW40JwJom13mNjY9PcyLnS9DPtmmZWzaLH46G+vj7l2xWklsw6GgUZw+TkJJ2dnYyPj2OxWFi7dm3erP7EnKlMu1hfKIn1iJFIhOrqatasWbPcu5VycsVZ1HWdgYGB+Oe1bt26WcOrk6K4Bu2yz6Dt+TTaqd9RdPgu/rLrAT7Fb3h5cBt3dlzFN/UtOKwq2xtKONBWydWtLgqsyxeMxYKumSLSMIz4yr3P56Ovrw+fzzetjihRSFqtVhG8C9KGYRg5s+iWyWSqWFyIZN3IxGtarPN0opBcLjfSTGdRpKFmPrkVDecxqbh4GIbB8PBwPNW0oaGBtrY2Tp8+nVNOzfmIpd3milicqx5xZGQkZ4OabHcWEz8vl8vF1q1bOXz48NKEYiKygrb6GoxVV6N5e1Ff/yk7X/8pu7Sv4rNX80zRjXxzcA9feMuNQ32Tfa0ubtpYxa7msrQ7jvNlSsQ6FDocjlkBRmJXw9HR0XhKa+Jqf0xI5mtKq3AWzUWkoaaHbBSL85GsGzk+Pk5/fz/BYBCY7kbGHmY2dTMrJhJiMTvIjWhYcEFEIhF6e3vp7e2lrKyM9evXTwtMFztrMdtRVTUnxmcsVI+oKErOfqbJjHvJREKhEJ2dnQwPD1NTU2Nq/ahRXEf40r8lvOuvsZz5HbbXfsJ1XT/ggPxjhlqu5Rfyfr7zlsRDx4Yod6rc0FbFTRuraFtZmLFiY76uhpqmxQMur9fL4OAggUAAeDvgSqwlypVFovnI1M8vFxBiMT1Eo9GcEYsLMZ8baRjGtE6t/f39+P3+aXNwZ9ZGXuhxadaxLRrcZAe5fVfMI5YSAExOTtLV1YXH41mwuUm+iUWLxZLVrzeZ+YiKosRXKHON2OiMbMHn89He3o7X66WhoYE1a9aYFnDOcuwUlejam4iuvQl59C3Uoz+h6o37+GToYf6sopVjK2/le+M7+dnhPv7zYC9NFQ4+sL2W92ytNrU5TiprsBVFoaioiKKiomnPx1JaY11aZ7bGn1kXmQsprWIcibkIsZgecslZXAqJM21nEo1G42n6y+1GJoPH48Hlci3rPgjOjxCLeUYs1bSrqwuAxsZG1q9fv2AQZLVamZycTNcuLjuxNNRsYuZ8xKamplkOSyK5Utc3F9mShjo2NkZ7ezvRaJSmpiY2bNiwrGJEr1hDaO+XCF32WdSTD6AeuYstx77Ct6yFTG67lUcLbuKutyx85XdvcffBXu7Y28Q1rS5T9jkd70NiSmsihmEQiUTiInJkZASfz0c4HEZRlFkpralYtU8XIg3VXIRYTA+appky8y8XsFgsFBcXU1xcPO35xHrvudxIh8MxLcMi8bpm5nUjHA5jt9tN2bYgdQixmCOc70SO1UH19fVRWlq6qGYZqqoSDodTsZtZQTaJxaXOR8ym17hYMlkIxxZr2tvbsdlsrFq1alaK0UL/Ny2BvlpAZNNtRDa+H7n/MNYjd1H4xj3cqt/FOxsv59Ur3sMX3qjj/7n/BJtri/ibq1exrT6517AYlssFkyQpntJaVjZ9JmUspdXn8zExMTFr1X6mG5lp7ocQi+YixGJ6yHdncSksVO8dcyP9fv+s65rNZsNutxONRhkfH0+pGykyHbIHIRZznJmppjt27Fj0iZ6PaaiZLqQudD5iJguqC0VRlIxb3NB1nb6+Prq6uigtLU1a1MeIpWWmNdCXJPSaiwnWXIx05RdRX/8p6ms/ZkfnHTxSXMerG2/hc+3b+NCPvexdW8HH99SzqaYoJfto1iigC2W+lNbEjoaxmZF+vx9d17FardNW7J1OJ6qqCtGWgwixmB6EWEwt53MjPR4PHo+HgYEBfD5fvGZ0rk6tizn+Y6NmxLUw8xFiMUdIPNkMw2BkZITOzk4Mw0gq1XQh8lEsxuYfZRrJ1CMmQy6LxUyqWYxEInR3d9PX10d1dTXbt29fUvqULMvLKp4MZyXhXX9FeOdfYHnrd6iv/pDtb/0fHrPYeb1hP/+943L++PQo9WV2bthQxQ0bqljlSl4MZzuJHQ0T628Mw4h3aY3Ni+zo6CASicSDrUQ30uy2+MJZNBchFtODEIvpIeZGRiIRiouLaW1tjf8s0Y1MbBwWm4U7U0jOZVKMjY0lnVkjWF6EWMwhotFovKtpSUnJ0ueyzSDfxKKqqhlVo6nrOkNDQ0nXIyaDxWLJGEGVajKhZjHR+a2vr2f37t0XFNzEXtOyB0iyhejaG4muvRF5+ATqqz9k04n7+bX8G/pXbuduruM7z63ju892sW6Fkxs2VHH9hkqqixdXk5KpzuJikSQJm82GzWabldK6UCMKh8Mxq0vrsn/2gvMSc0oE5pIv3VAzhblmLCZbGzk4OIjf748vkD300ENomkZrayulpaUpn9/9yCOPcMcdd6BpGh//+Mf53Oc+l9Lt5ytCLOYIhmFw6NAhVqxYsaRU04XI1lEESyVT0lCXWo+YDIqiZMRrNIPldE29Xi/t7e34/X6amppobW1NWVpmKs7BVAayeuV6Qvv/N6HLP4/19Z+y4shdfMb7P7nDVcdB17v5pmc3//JkO//yZDvb6ou5cUMVN26swmk7/20nV8TiQswXbOm6Hm+L7/P5GB0djae02my2WW7kYq71wlk0F8MwhLOYBmID6wXpIRKJJP1+n6820jAMXn31VQ4fPszx48c5ffo0W7dupb6+ntbWVtatW0drayutra24XItroKZpGp/85Cd57LHHqKurY8eOHdx88820tbUt6vUKZiPOthxBlmV27dq13LuREyy3WLzQesRkyPU01HQubhiGgdvtpr29HUmSaGpqory8PKVB+XKnoS6Io4zwzr8gvP2/YTnzKOrhH7Cn/ZvsVr+Pe+ut/Mp6I3e/FeEfHnmLrz/Vwfu3reQDO2pxFYpuhnMhyzJOpxOn00llZWX8+VhKa6xL68wV+5nNdeZKaRVi0XzE+2s+Ig01vczlLC4Fi8XC9u3b2b59OwAPP/wwr776Kl/5ylfo7u7m1KlTnDp1invvvZdTp06xY8cOvvKVryS9/Zdffpk1a9awatUqAN7//vfzwAMPCLGYAoRYzCHMXo3Pl0BjucRiquoRkyGXP8d0OeG6rsfHlRQUFNDa2jqr8UmqSJWzaCqyhWjLDURbbkAePIb18PcpP3kvH9P/kw+tupqTOz/AN8/W8v3nu7nrpR5u3ryCD++qp7HcMWtT+eAsLpbElNaZqVuJKa1jY2P09vYSDAanzWNzOp1omoamacL9EmQ1Qiyml0gkkrKspkQ8Hg/l5eXIskxjYyONjY3s379/ydvr7e2lvr4+/n1dXR0vvfRSKnY17xFiMYcwM8CK1bjlQ+pHOms0zajVgTdTAAAgAElEQVRHzHfMbnATqw3u6emhoqKCLVu2mD4nKpVuaToWffQVGwle/3WkK76AeuTHqK/9hE1nH+c7levpu+ZDfGt4C786Osj9rw5wzToXH9lVx6ba4vNvWDAn50tpjbmRoVCII0eOYBgGNpttlhu53AO6BYJkEOm+6SU2izHVuN1uqqurU7a9ueLfXF4YTye5H/kLUkJs1mI+iMV0pGiaWY+Y75jlLIbDYTo7OxkcHKSmpoadO3emLbjO6DTUBTCcVYQv/QzhSz6FeuJXqIe/T/2zn+N/OVfw2T0f5Eehvfzw6BiPnRzh0lVl/N21q1nlKhDOYopITGkFGB4ejqeAhUKhuBuZ2BLfYrHMGvVhs9lE0CUQ5CmRSMSUe53b7WbDhg0p215dXR3d3d3x73t6eqipqUnZ9vOZ3I/88wgzb+b51BHVzPcxHfWIiyEXU4tT7Sz6fD46OjoYHx+noaGBPXv2pH1VOyvSUBfCYiey6TYiG9+P0vkHrIfupPzg1/i05dv82ab38gvLO/jq4QnefechbtteyzXVhhCLJhE73+12O3a7fVZKayQSiYtIj8czb0qr0+nE4XAIh0cgyHHMchY9Hs+sJjgXwo4dO3jzzTdpb2+ntraWe++9l3vuuSdl289nhFgUJEU+iUUzSGc9YrJkzDiGFJMqZ3FsbIz29nYikQhNTU20tbUtm7DOhHEgKUGS0JquJNB0JfLISdRXvkfB8Z9xu/afvLf5Wv7DuImvHYTfWCX+/FI7t+0qwiLn1mJGpqOqKiUlJbPmn+m6Hm+HH5sZ6ff7p81VS0xrzYcsFMHyIBaS0otZzmKqxaLFYuFb3/oWBw4cQNM0PvrRj6bUucxnxNU8hxDOYmq5UNct0+sRY+m2uSYWL8RZNAwjPjhdVVWam5sz4jNLVVpmJrnIumsdoQNfI3zZZ1GP3IXjyF18KvgoH6rbwte91/DV32v8/Ogof3llE9euW1wLdUHqkWWZwsLCWbN7Z85V6+/vx+fzxWvcYy5kTERardac/CyFgEkPuq4v+0JrvmFWnJBqsQhwww03cMMNN6R0mwIhFgVJYrVa80osxoTUUlbHZ9Yjbt68GYdjdsfH5SbWtCjXWEp9n67r9PX10dXVRUlJCRs2bIjXeWUCOeMszsFUXePfEt75SdRjP8f5yvf4Yuir/HVZHT+I3sjf/3IXP6iu4I69TexuLstJoZHNLDRXLRKJxJvrjI6O0t3dTSgUQpblaSmtBQUFWZ/Squu6ODbTQC4ucGY6ZpWrjI+PU1ZWlvLtClKPEIs5hNnO4uTkpGnbzzRi4zMWIxYzrR7xfCiKsqzzJDOBSCRCT08PfX19VFVVcfHFF2Oz2ZZ7t2aRrQ1uFoVaQGTrh4lc9CcM/eEH1HX+kr8e+S5/XvQzfuI9wGd/uo+Wxjru2NvMRaJzalagqiqlpaWz3HlN0+JdWicnJxkcHCQQCMRTWmd2ac3k62gM0aEzPUSjUSEWcwDDMNB1PSvObYEQi4IkiXVDzRcWM2sxE+sRkyEdXV8zlWAwSGdnJyMjI9TV1WW8sM/6BjeLQVYYr92Luvk9uPynsR78d/707M/4cMED3De0j7/70XXs3LyBz1yzihKHGPWQjSiKsmBKa8yN7O3txe/3o2kaqqrO6tKaSSmtIj0yPQhnMb2YeVznYoO9XCVzoyPBohE1i6njfGIx0+sRkyEfxaLX66Wjo4PJyUmamppoaWnJigAvL5zFBCRJmmqGU7eLQN0u5JGTWA9+h9tO/pr323/HAyd28zdv3cJt11/N1etcy727ghSRmNI6k3A4/LaIHBzGO9mJpIVRLcqs5jp2uz3t57UQi+khX+Y9ZwpmdUINhUJYrdaUb1dgDuKMEyRFPorFuV5vttQjJkOu1izOxDAMPB4P7e3tGIZBc3Mz5eXlWbWimcs1i/ORKI511zqC138d6dK/xfrK97j56D3cEn2Wx3+zlW8fvp333fxOXIUi8EiWqG7gC0XxhzV85x7+sIY/9Pa/48/FHhENX2jqayCsEYzqBCMagcjU14hmUGy3UOywUGJXKXFYsKsyvpCGNxRlMqQxGYziDUWxWWTaVhbRVl1I28pC1q0oRJJgPBBlPBBlIhhhPBDF448w4gvj9kUYmQwz4gszMhkmEHn7XLAqEg41hE0Zw6ZAgQWKVYMyO7icVqpL7DRWFLKloZyS4sIpV8owwNBBj4CugR5F0rWp7w19xkOb+v1zSDMWbQxJBgmkYBhHcAhpvBtkBSQFZAtGwr9RrFM/EywZ4SymFzNnLM4c2yPIXIRYzCGEs5g6VFWdJqSyrR4xGXK9ZtEwDAYHB+no6KCgoICWlhaKi7Oz1i1VaajZIpDn6/5qFNcS2vs/YNcdKK/+iEsPfp9r+j/Noe/eyenNf862K9+J3Zrd52UqMAyDnrEgr/VO8FqPl+MDXsb8EcZ8QcJPPkswmtyxJAFOm0KBqlAQ+2pVcBVasasydlXBYZFxWBUUWcIbnBJ748EIw5NhghGNQpuFQpvCiiIbRTYLhXaFyaDG8QEvP3qxh6j+9uesEsVJgEIpQCFBnASoskWpsUfZYotS7oxQVhKm1BJBNUIQCSBpQaRoACUaRNbCSJEQUjCENBbCaoSxSRFUoliJYpU0VCmKxYgikVqnvhBwATyz8O8ZkgyyCoqKIatgsYJix7DYpsSkYsNQ7WBxYFjsoDowLI6p760FGKoTrIUY1gJQnRjWwnOPIrAVYVgLwWKHLDnXF4sQi+nFLGfR7XanvBOqwDzEXTXHSFWL/ZmkanZdthBzFrO1HjEZcjUNVdM0wuEwzz//POXl5Vx00UVZ6/7GyEdncUEcZWh7Pg07/ozeF+6i6ZXvsv3oHRw/+nVeq7+d1iveR0t1di4MLJaIptPtCdI+6ufsiJ+jvV6O9k3g9k0t7hVYFTasLGRDTRH+8QhNtStx2hSc1nMPm0KB1YLTOiUE419tCnaLvLgFhmgQKTh27uGH4ARSaBwpOP7217AXtAmkYi/YJoj4x5FCXtSoD8WYZ0EyeO6RgGGxgcU+JaRUB0aBfep7xQmWcgzFRlS2EtAtjIdl3prU6RqPMhaWCGNBMxT0c46fLMtYLQplBSrVxTaqih2EUPGEJIb9OmNBHVWRsVlkrOceNotMkV2hwqlS4bCgGmEGR0bRrEX0evz0j/nx+oPoWhRd1zC0CJIWwSJFsaJRYjUotUGprFNs0XDIEbRgkGgkCBEPUrQfix7EKYcpkMI4CGEzQkl9DJpkISAXMik5GTcKcOsFjOkFOIsrWLlyJbUrVyI5yjDsZRiOMoyCCgxHBVgLM15kigY36UU4iwIQYlEgmIWu60xOTjI8PExJSUlW1iMmg8ViyammReFwmK6uLgYHBwHYtm1b1ovEGHnV4IZFLHqpBRRf8QmMPR/lxHP3UPHad7mt+0uc/cl3+WHRH+HadRvXbKjBoeZGcBmO6jx31sPR3om4OOz2BKe5c03lDi5bVcZFtcVcVFfMmkonijwlAA4ePMiOHauS+2NaGGlyCCngRvKPTH2NPzxv/zvoQQqMTX2NBhfcpGEtwrAVY9imvlK4Akv5GgxbMVFrIdG4S1YI1nOumeoEteCck3bOWbPYk07nVJly/FzAJsOgfTTAoc4xxgLn0nBDUSbDGt3uACcGJ4kMTT/unCq47BJRQyKkSwSjBoGIjjbj8FRliYjeCEw5sqsrC2iuKcBhnXJf7aqCXZWRVBlPROfYWJDec4+hyanrsCJBdbGNleV2akrtVBZa8fgi9I4H6fEEGJoIYDVCFBDEKQVxMvUokvwUEqBIClBIgGLJj8sSoNISpNziZ6XkZ7U2isV7jJKJSZTTc59bUUklpJYRsZehF1QiF1aiFFWhFFYiFVVhOFdgOKvQC1eAtWhZhKVwFtNLJBIxxVk0Y8aiwDyEWMwxzHIWY+Ry96rEekSHw0FlZSVtbW3LvVumkStpqH6/n46ODsbGxqivr2fXrl28+uqrOeMAw5SzmE9p4Iu9xkgWG3VXfgQuv53hNx6k6Llv8Fe+b9Lz+D187/GbCW54H7dc3ERLVebMzkyWiKbzYvsYjxwf4snTo0yGNBQJ6ssdrKooYF+ri1UVBTRXOGh2FVBom/+2LuthpPFuJN8Qsm8YyT+M5BueEoP+YSTfCHJgBMk/ihSamHMbBtKUG+Uox3CUoxfXQ9VmDHvp1PP20nOPkqmHbeor1qJlr9eTJIlVrgJWuQrm/HlE0zk16OOtYR8rim20VDqpcKrTurTGHuOTftwBDU/EwnjUwqBPwy7rXLW5iS31ZTgX+BxmEorqjAcilDutWOT5j/2IpjPoDdHjCTIejGKRJVRZwqJIWGQZq0WiwmmlstCKfY4Fkoim819vjvDqWz1ofg9SwIMa8mALn3tExiiPeKkIjOMa68MlnaSScWzS7GtPWLITKahELalBKl6JXrQSo3AlRtG5fxfVYhS4Ui4oNU3DbrendJuC+YlGo8JZFAixKEieWIdQMy4cy4nf76erq2taPaLX62VgYGC5d81Usj0NdXx8nPb2dkKhEE1NTaxfvz4uMnItbToV3VBjc61iCwSyPJViKElSRgrrJb1eWcG+6Z2w8Wb8Z5+k6Jl/5e9H/4PhN+7ne6/dwDdqb+W9u1q4fE05cgYvemm6wcHOMR45Pszjp0YYD0Qpsilc3eriurZKLmkqRVUSPrNoEGlyEHn4JJJvCMk3MPX95CCSbxBpcgjZP8RVwXF4dvbfM+yl6AWVGE4XWuVGDKcLw1GBUeDCKCjHcLimhGFBBdiKl130mYWqyGysKWJjTdG05yVJio/sqKysjD9vGEa8S+vQ0BBerxeLt4c3XmtHUebu0jrXQojNIlNVdP75rqoiU1fqoK50aRkTqiJz9boqrl5XNefPo7qBxxdmxBehbzLM0ckw3mAELTiB4h9BDQxhC44g+wYJj/VTOeGm2uuhQe3EpY9imZFGbCg2jOIa9KJa9OJajOJ69JJ6jJIG9OI6jMIVIC3u2iOcxfQSiURMEedut5uWlpaUb1dgDkIs5hjpaHKTK2JxZj1ia2tr/P2brxtqLpGN3VANw2BkZISOjg4URaG5uZmysrJZvyfLcta9toW4kDTUmEiM/X9VnXJKYs8D096rmIBcThF5wRkSkoS2+mrkVfvw97xA0fPf4As9P2V86L/43v3X8+/F7+RdO9dy8+YVFFiXL/CcDEXpcgfocAdoH/HHv3a6AwSjOgVWhf1rnNzcqLG9dBLV/xryUB/S2QHkyX4k7wDSZD9ywD1r24ZifTttsGINWsMeejwRalq3ojurMJyVGAWVGAUVU41VBItGkiRsNhs2mw1N07DZbDQ3NwNTjozf759yIcfH6evrIxgMxseDJIpIh8OREQLIIktUFtmoTEK4BiMah7vHebh9jOfPejg9NEk5XlZKbmrkUdZYPTTKbup8o6z0jVDdfwJnZHTaNgzFNiUeSxvRSxrRS5vQSxvRy5oxiutBmR1rCLGYXsx0FkUaavYgxKIgaXKhI2qy8xHPN2cxF8imNFRd1+nv76erq4uioiLWr18/a6B3IrnWEGYpr2emSJxPAMZ+ruv6rP8zn4iM7VPGI0lo9XvQ3rcHrf8wjhe/yWfO3sefBx/mB08c4Nanb2L/1hY+uKMmqQB5KUQ0nbMjU/WFne4A3Z4AXZ4gXZ4AY74QVXiokUapk0e4yDHOrbYx6stHqWaE4vAQ8tkxODt9m7qjAqNoKuVPq9mGUViNXliNUbgCw7kCvbAa7KWzUgA7Dh6kctMOU15nvjNzzqLFYqG4uHhWB2Zd1wkEAnEhOTo6it/vR9d1bDbbLDcyUxdn7arCnlXl7FlVzt9cDSOTYQ51jTE8GcbjjzAaiPKWP8J4IMKQN0yHO4CNMKvVUa5wTbK9ZIK11lFWaINYJjpQu19Aivjj2zdkC0ZJPXrZKvTSZvTy1ejlq5H8Eoo8tzMqSD2iZlEAQizmHGJ8xtwsdj5ivojFTHffotEo3d3d9PX1UVlZybZt27DZzh/UZ8NrWwzJpqHGfmcukbjQthO/xoj9/5iATHQjY7XLhmFMS2edaztLwYzaa33lNkK3/IjI4DFsL36DO976Jf9NeoQfHryGPz54EzfsXM9HdtVR4lh6cO4LRTk74ufE4CQnBiY51T/OxHAP1foQddIwtdII11pHabaMUi0PU+YYQjESjtMoGJYS9IJajKIGokW7E2rAatCLajAKq8FijrAVLJ2ZYnE+ZFnG6XTidDpnpbSGQqG4iBwcHMTn88VHFySKyIKCgnlTWpcLV6GV69rmF3FuX5hXusc52DnOE13jfOekDwBVkdi4sohtG4vZWRmlNNSLfaIDx2QXBZMdOIc7Kep8Dqs21TxpKxBRi5BcLRjlLWgVLeiutegVrRhFNRnfzTXbMMtZFGIxuxBiUZA0Vqs168TiXPWIyayS5YNYzOQ01GAwSGdnJyMjI0uaa5lrzuL50lBjwkrTtPi/zycSz0di4Dsz7SvRhVwopTUmJGdu73yY2ahLX7GR4Du/R3j4BNaX/g+fOPVffFz6HY8e3MrXDu+heec7eN8lq+ZMTzUMg9NDPg51jTM4EWLIGyIwMYLq7abQ38sKbYB6aYhWaYhrlRFqGMWiTr+O6AUrMIrr0It3Ei2pI1JcN1XPVVSLXlQDtqJZf1eQ+SQrFudDkiTsdjt2u31W449IJILf78fv9+PxeOjt7Y2ntMbEY6KQzETXv9xp5dp1lVy7bkogjwcivNo9weHucV7pHueul3r5gW4ACrD63COGwUrcrJb7WC31sSbay9q+floHH6VU/1n8t8JKAe6CZkYLVjNSsIYhxyr6bavwSkVEdANNN9hcW8zlqxfXgCifMctZdLvduFyulG9XYA7ibMkxhLM4xUL1iMmQSSu2ZpGJaaiTk5N0dHTg9XppbGykpaVlSYFPvjS4men2wYWLxGT3B5YmIme6kcsV2OqV6wne9G/Iuz+N+uoPOXDyQW4KvcjkS//GMwe3I7e9ix1734kvInH05Ek6zpxgvO8tysN9NEoDXCEP0SANU8i51Dl56hGylqGXNGAp34lW0kC0pB69uAG9pG7K+bCITo65iK7rpgTVMHXvLSkpoaSkZNbfjIlIn8/H8PAwgUAAXdex2+2zhGQmpbSWOFSuWlvBVWun3KVAROPU4CSazrnurlMPVZGRJDAM0A2D1984jlRWx897vBzuHsczOkSL1MtauYc10V5aw92sm3iSDdJv4n9rwCjjFE0cNxr5/aEG7pSaqG1ax751VVy1toL/y96bx0Zy32efT5/si/fRPPskh8MhqTk1k1E09pvDTlY2rHVevLCEje3XiTaOgMSxjcQK1pqBJ44OW4HlDRI5SNaOFoiQXUtxYmwg21kvbCexDttxRppL0pBd1Xc3yb7Y91FV+8e8VSo2rybZ1V3H7wMQlDgz3dXsrqrf8/t+v88zaJPP70VusCwryYxoqVTac5SEIC+IWCS0jMlkQqFQ6PZh7Eqr84iEu8ip+pbJZEBRFBiGgdfrxeLi4pGrYnKtmh6G5spisyBrnifsFq2KSP5nwM4ikv//TsAOz6H6q08Cv/wnqIdfRf4/XsL99L+g9+a/o3Tz83BwDXxA9+5niTGZwPS7oBucBTfwy6j0u8H2u8ANuO7GSJjvxnPIaxuGIDVHrSweBr1eD4fDsW3Rzbe0FotFlEolxONxlEoloaVVPBNps9nQ09PT9WuH1WTAqen+ff9exg6cu2ccD56cAADkKw00WA463O1A1el0qILDWmkd5vTb6Mm8jeGN27h//Rbek/pn6PR3z8xi1IKbYTf+v+95UBpewszCvTh3+hx6bWQzR2rEG5sEZUDEosqQurIoxxD3g84jHgQ150p2+3VxHIe1tTXQNA2LxYLZ2dltZhCHRY2VxZ0MaOQae9HMXiKS/84L31wuh7W1NUxPTwudDB1xaNUbwbgvweG+BK5Rw09/8l0UbnwXVnsfhmfmMOE+Dgx67s4MqjQ6gnB4uiEWd0Pc0to8F8a3tBaLRaTTaYTDYVSrVej1+h1dWuXymsSI7129ll2WsZZJYGgSDfzSuxs3jSr0qTvQr9+EMXkDC9E3cCr1I5hz3wNeA8qvmhG1zAKTp+E8dgG6qVPgBryanYOUasOOiEXlQcQioWXk1oZaKpUQDAaRTqcPNde2H/wCndh0txeGYRCLxRAOhzE4OIjl5WXYbDuHZB8WNVYW+UqB2WzeUoFTMvxCVKfTCdVlo9GI+fl59PX1dc2hVWc04/h9HwLu+5Dws87UOQlKRU5icS92a2llGAblchnFYlHIjSyXy+A4DhaLZVs1UqqW2/04koAx9oB1LoF1LgFLHwEAVFkGtfQqYm//BOt3fgZ76jrmAy/CSr0AAMjrHAhbj2Ojbxn18dPwLP8ixsac7XgpsodhGEne50KhQFpQFQYRiypDCzOLmUwGwWBQmEc8fvy4JK/bZDKh0WgQsdgmarUawuEwEokExsfHce7cOZjN0uS7qUUs8kLJZDLB4XDg9u3bqNVqQuC3w+EQnBXl5o7YCuLcTKvVivn5+S2LCDk5tCqdTrX1ahWWZRV3/okxGAy7trRWKhWhGhmLxVAsFsEwDEwm07aoD7PZrKzfg94AbuQYJkaOYeIXfxMNlsO/BdYReucN2FLXMbp5E57yW/jF4vMwJP4WuAaEdZPYGDwJi+cCJhbvh2H0GKBT3zWGb1tuN6lUapuJE0HeELGoQqRyEuymWOzGPKLRaES9Xm8pqkHJSN1qWy6XQdM0MpkMpqen8Qu/8AuSC3CDwSDLlulWaa6mGQwGHDt2TPhzPvC7UCggk8kgEomgUqlAr9cLiza73Q6HwwGr1Sq7xRvHcUgmkwgGg+jt7cXi4mJL1eV2ObQCymnhbRdqbqmXA/wmhdrQ6XSwWq2wWq3bWlprtdqWvEhxS2uzuU47Wlo78Rk26nW4ODuGi7PvA/A+4ef5Sh7Jd36C1Nuvwpz4OXypf8NQ+jvAz4GCzoH1gXtgcP8CBucvARMnAYM0G6GdpF6vk9gMAgAiFgkHoBtzYFLOI+6HFuIz+PdUCvG2ubkJiqJQqVTg8XgkqwDvhBJnFg+Skbhb4DfDMMLiLZ/PIx6Po1wuCws+cSWyGxb7LMsiHo8jHA5jaGgIJ0+ehMXSHkOJgzi0iqNGAPk4tBKUi1LaUNuJ2WyG2WzetnHLX4dKpRLy+TySyaTQ0mq1WrdFfbRaverm79hg6cXkPb+CyXt+BQBQrNTx/ZtvIPPOq7Ct/QfmU7fgzbwCXPsKajoz1nqX0Ji+gP7598A4cw4wdWbd0k5IZZHAQ8SiCpEyo6xTSD2P2ApaEYvtbLXlOA6pVAoURcFgMMDr9WJgYKDjFQ0ltaG2M/7CYDCgt7cXvb1bs/p4i33xPFKpVBIWb3wVkl/AtXvzgGEYRKNRRKNRjI2N4cyZM5K1IDdzGIfWRqOxY0urksUAqSxKixbF4m7sdh3iOA7lcnlLZmSpVBJaWpvnIptbWhmGkc1YiN1iwoWz54Cz5wAAa/kq/uHtAHLv/Bj2tZ/hRPYGTuT+CoZbX0MdRoRtiyiOn8fIif8Ch/+CIiJ0pKwsErGoLIhYJBwYKRcdnZpHbAWtiMV2iCqWZZFIJBAMBuFwOLCwsNDVAXY5xYLsRifjL/ay2OdNLQqFAjY2NlAqlYScNr4KyX8ddMOmXq8jEokgkUhgYmIC9957b9eMMZo5iENrJ811CMqEiMX90el0QjVRDMdxqNfrQtTH+vo6SqUSarUa9Hr9NlMdOf6ux3p78P5zC8C5BQCPIFWs4V/oGDbv/BjW+E/gLf4nTqz+HzAE/gaMvgfc9L1gXPej4fpFsM57ZOmwLFVlMZ1OkzZUhSGPuzahrUgprngB1c7dJrnmIxKxuD/iNuGRkRGcPn26bW2FR6FdIlgK5JSRKF68jY6ObjnGSqUiVCKj0ahgamE2m7dUIu12+7brQa1WQygUwvr6Oqanp3H+/HnZVAT2g1+EtmKuI96Q4D9vchWRpLIoLXIUMEpBp9MJLa2Dg4Nb/qzRaAgbWplMBsViEf/xH/8BADu6tMrlOjNsN+P+RQ+w6AHwv4BhOfw8FMc/vfxt+PM/x4OpOxgOPY0eAFxPPxqu+8C434uG5z3g+l3dPfj/Qb1el+R+nslk4PF42v64BOkgYpFwIHiTm3aIxW7OI7aCyWRCtVrt9mFIymEFcbVaRTAYxPr6OiYnJ7vSJrwXcqwsKikjUWxqMTIyIvyc4zjUajWhEhmPx1EsFoUNJIvFgnK5jEqlApfLhQsXLsj2NR6U3cx19nJoBe6KSF6oiSNPOv17IWJRWohYlAaj0Si0tFosFsHsi2VZYUOrVCohnU4LXRH8hpbYZMdkMnX182/Q63DcM4nf/+3/FY/901v4k5U0/ie3Dv91cAVnmDcwkHgFpjvfAQCwAx403O9Fw/tfwLh+ETC1N1qqVer1uiQdQul0est9hSB/5LO6I7QNucdnyGEesRWMRiOKxWK3D0NSDlqBKxaLoCgK+XweLpcLs7OzslwgycngZieRqNRFu06nQ09PD3p6erbMnBSLRayuriKXy2FgYAAOhwPr6+uIxWIwGAzbKpE9PT2K/R00c1SHVjXNRWoZIhalRzyzKHZcFcNvaPEz2uvr66BpGvV6XYgcElcjOx05ZO8x4n//b4v46x+H8O03EvhO0A/AD6fjI/iQp4j/2XEbc8WfwXTzmzC/8X+CM5jBTJ1Hw/tLYLy/BHZoDujQ8ba7i4yHuKEqD/mt0Amy5ihiMZPJgKZp1Gq1rs8jtoIW2lCNRmNLYpF/7xqNBjweDxYXF2X93snB4EZNInE38vk8KIpCrVaDx+PB8PDwttfIzyLx9vqhUEiw1xdHfCg1K3IvDuLQKrWIJJVFaSFiUXpaMbgRb2jt1NLKi54/uAQAACAASURBVMhcLrfNLbrZpVWqllaDXodHL7nx6CU3wpkyXqOyeI3O4P+mOPxN5SSG7OfwoYU/xkPOCHy512CgfgjLj74I/OiLYPtm0PD9Chq+XwEzc1FSo5x6vU5mFgkAiFhUJVIuCMxm84HEYvM8Iu+OqQS0IBZ5N9Sd4DgO6+vroCgKPT098Pl86O/v7/ARHo5uVha1IBKz2SwoigIAeDyebYsyMSaTCQMDAzva6/MiUpwVqdPpthnr2Gw2Vf0OWxGRAFoy1zmIQFHT71BuEDEuPUd1Q90tcohlWcGlld/U4ltae3p6tlUj21ltmxm0YmbQiv92ZgJ1hsW/raTx/1xfw9/9fAPPsz1wD/065p3/FaenC/gF5ufw515B743/C+Zrz4MzWlF9z/+G+ulPtO14xEhVWcxms0QsKgwiFgkHwmQytRR2zrsgxmIxWc4jtoJWxGJzBY5lWcRiMYRCIQwMDGB5ebmlwHQ50enKoji376jxF3KF4zik02nQNA2TyQS/379t0XUQDAbDrgs3XkTm83kkEgmUSiVh97855kNN1RwpHVqVHqekBNR0vsuRdsY8iRF3OTQbffEz2qVSCclkEqVSSWhpbTbXOWpnhMmgxy/Pj+CX50eQLdXx3VvreIXK4HaigP/3dgUcTgA4gT7jf8fvuaP476NvgR2abcNvYGekckOt1+vo6elp++MSpIOIRRUi9cxipVLZ9c+VMo/YCu2Yz5Q7BoNBMPGp1+sIh8OIxWIYHx/HuXPnOpaF1246ZXDTzoxEucJXmGmaht1ux/Hjx2G32yV7Pr1ev2tWpDjmY6esSF5IyskVsR20w6GV/2/SLklQKgzDdFRk7DajDdy9X4rzIqPRqNAZITbW4f/7oOfcgM2Eh85N4qFzkwCAUo1BYKOEO+tFrKwXwfXPo3rvR9v2WndCimo52bRSJspcxRO6xm4CSmnziK2ghcqi0WhELpfDW2+9hVQqhZmZGVy8eFHxC22pP3tyir+QCpZlkUwmEQwGhQpzN7sDxLv/Y2Njws/FWZE7tZCJjXUOkxUpZ3Yz1+E/l/znNJfLgaZp9Pb2gmGYLdXIbjq0EggH4ahtqO3EZDKhv79/22iGeFOLN9gpl8vC9ai5Gtlqm6fNbMDSZC+WJnv3/8syhmGYLdccgjJQz12TINApN1QlzyO2gtovZvl8HsFgEIVCAQsLC5ifn1f9az4qO4lEtS2wGYZBPB5HOBwWsjPl3DK0V1ZktVpFoVDYNStS3NIqxWxOt+A3LrLZLAKBgBA30NfXRxxaCYpFTmJxN8SbWmL46xHf0ppIJITYIaPRuC3qo9uO0SzLSvL8mUxGVetErUDEokrR6XSSlPv57EGKohQ9j6hV+LkziqKg0+kwNjYGq9WK8fHxbh+arFFSRuJh4XNP4/E4nE4nzp07p2gBpdPpYLFYYLFYds2KLBaL27IixVVIh8PR9Xy2w5DJZEBRFAwGA+bm5ra09MrJoZVAOAhKEIu7Ib4eNZu78C2tYrMv3jGab7HnRaTVau3IeSfVvCJxQlUmRCwSWqZUKoGmaWQyGYyOjip6HlFriFsKbTYb5ufn0dvbi0KhgFwu1+3Dky1acDat1+sIhUJYW1vD5OQk7r33XlWf13vNIYlFJD+nWavVFJMVyW8EmUwmHDt27ECB2vuJyObWVqA9Dq0EQqtIZXDTbXZraWUYZotL6/r6ujCnbbFYtrm0tvO6LZUTajqd3nbdJcgf9a4INE47K4vN84iZTAYej6ctjy13eFdNpd6gGo0GotEoIpEIhoeHcerUKVgs7+Yy7RWdoWW0IBKr1apgRjU9PY0LFy5ofpFvNpthNpt3zGfbLyuSF5OdzorkOE6oJJrNZszPzx9IJO7Hbp+JZodW8fnSqkOrWiCmHZ2BYRhVb2Q1YzAY4HA4tp3PHMehUqkIIpLvjmAYBiaTaZuINJvNB74m1et1ycQiqSwqD+2cdYQDsdc8YiAQ6PLRdQ7e5EZpYrFWqyEYDCKZTGJychLnz5/f8cK/U3SGmjiImxu/4FO7SCyXy6BpGpubm3C5XJidnVXlAr6dGI3GXXf+eRGZy+W2OCI2Z0W2u31M3FJusVgkd6lt5iAOrc3VyOZ21p0eR0kQh9nOoOSN23bCxwhZrdZtwqtWqwkuralUCuFwWNjYanZp3euaJFUbaiaTIZVFBULEoko57AJXnI84MjKy6zyiVgKIebEoZ4MPMcViETRNI5fLweVy4b777ttzEaNmx1eDwQCWZfddXGghIxEACoUCaJpGuVxWjWNxt9krK7JUKqFQKGzJigQgLNYOmxXJcRxSqRQoioLVasXCwkJHReJ+7ObQCrQ2F8k/hpJEpFRmIIStEFG+P3x3RLOJDMMwgojM5/NIJpMol8tC9FCzkJSqsphKpTA9Pd32xyVICxGLBAAHy0fkBYaSzS9aRSliKpvNgqIo1Ot1eDwenDhxoqXFi1RGSHJgvxZiLWQkAsDm5iYoikKj0YDH48HQ0JDqXqPc0Ov1O7aPNdvq75YVyX81x2HwItFms2FxcRE2m63TL+1IqNVchz82grRoZZNaCgwGw475tXxLK+/SGo1GUSqVUC6XYTQaUalUtojIw7S0islkMjh58uRRXw6hwxCxqFJaPZnF84gej6elagMfn6EFsWgymWQrFsVh6SaT6VDRJWq+8er1+i0B5TxayEgE3nXE1Ov18Hg8xK5cBuxlq1+pVISYj3Q6jWKxKGSz6fV65PN5OBwOzM/Pb6tkKh2li0hS8eoMartGywFxS6uYQCAAq9UKi8WCUqmEjY0NFItF1Go1oaVVPBdpsVhaOgfIzKIyIWJRg/DOmKFQ6FD5iOKsRbVjNBpl91pZlkUsFkMoFEJ/fz8WFxdl1YYmF5rnMbUQf8FXn2iaRk9Pz7bYBII8ES/Y+KxIjuOwtrYmGNeMj4+jVqvh7bffFlrj1ZwVCewtIvnvcnBoJWKxM6i1C0aOMAwDi8WCwcHBbYZffEtrsVgU2uwrlQoAwGKxbBGRNptty/mbzWaJWFQgRCyqlJ124FqdR9wPrYlFuVQWxe/f2NgYzp49q5hZym7AVxa14GzKC4tgMAiHw4ETJ04orkWRcBfxe9nb24uTJ09uu043Z0UmEgkUCgXBlEIc8XFYN0Q5s5+5TqcdWolYlB7SgtpZ9uoe262llWXZLS6tmUwG//mf/4lnnnkGw8PD8Pv9SCQSeOuttzA4OIjR0dG2vacvvvgivvCFL+D27dv4yU9+gnPnzrXlcQl3IWJRAxxkHrEVzGYzarVaG49QvsihslipVBAMBrGxsSFEHLTbpUyNN2KDwYBqtSpEhahRJLIsi0QigVAohMHBQdxzzz1bolEIyoEXiTRNo7+/f8/3cq+syHq9jmKxiEKhsGNWpLgSKcesyKNwGIdW/tp3FIdWIhalhzihdpbDuKGKHVdHRkYAAAsLC3jooYcQjUZx/fp1PPHEE/j+97+Pv/zLv8T6+jrsdjuOHz+O48ePY2FhAb/+679+qPd5aWkJ3/rWt/DJT37ywP+WsD9ELKoUnU53qHnEVtBSZdFkMqFcLnflufP5PCiKQrFYhMfjwdzcnCQLEr5dUy35VfwicHBwEHfu3AHDMOjp6REWyPx3Jb9ehmEQjUYRjUYxOjqKM2fOwGw2d/uwCIeA4zgkk0kEg0EMDAzg5MmTRxL8JpMJAwMD20YLxFmR6XR616xIPuZDjSISkMahlYhF6SFisbO005dCr9djZmYG09PTeOqpp/Dnf/7nwrlUKBTw9ttvCxXBBx544FDPsbCw0JZjJeyMcldLhD2p1WoIhUKHMj3ZD5PJJPSnq51OVxbFAdscx8Hr9UruXsm32ipZPO2UkTg2Ngan0ym07PHmIdFoFMViUZj7UpKIbDQaCIfDSCQSGB8fx7lz51Q3p6YVOI5DIpFAMBjE4OAgTp06JWlb+V5ZkXzMRy6XQywWQ7lchk6n2xbz0e6sSDnQDnOdRqOhKnEtR4hY7CwMw0hyrjd3MTkcDpw9exZnz55t+3MR2od8V0WEI9HT0yOZPbGWKoudmlnkqws0TcNms2Fubq5jjofNRjBKopX4C3HLnniwXkkikt/8WV9fx9TUFM6fP08WTgqFNxgLBoMYGhrC6dOnuzp7vNf8UbOJRXNWJH9+HDQrUgm0KiI3NzcRDAYxNjYm3Bfl4NCqNhqNBrnmdZh2b4CUy+UjdU386q/+KhKJxLafP/HEE3jwwQePcmiEfSBiUcVIlaFHxGL74NsJw+EwhoaGdjSzkBolisV2xF8oQUTy86qZTAYzMzO4cOECWXgqFPF86fDwsOxbh8VZkU6nU/h5c1Ykb6nPcRwsFss2cx21LfD5869UKmF1dRUcx+H48eNCpqZcHFrVhppGJbRKOp3eNmN9EL7//e+38WgIB4GceYQDQ8Ti0eErRYlEApOTkzh//nzX2gnl5Pi6H53ISJSDiCyVSqBpGoVCAW63G8eOHSNtbgqFZVnE43GEw2FFiMT9OGxWZLO5jlIX/oVCAYFAAI1GA36/f1tbr1wcWtUGaUPtHFL9ro8qFgndQ5lXa0JLSFVZNJvNRCweEl4EZLNZuFwu3HfffV1fFCihsiiHjMROiMhCoQCKolCpVODxeLCwsEBEokLh81AjkQhGRkZw9uxZVc+X7pQVCdw9P6rVqlCJFJ8fZrN5x5gPOVIqlRAIBFCpVOD3+7dlz+1Gtxxa1QYRi51DKg+DdDotWcbiP/7jP+L3f//3sb6+jg984AM4deoUvve970nyXFqEiEXCgeHz67SAXq9vi+DO5XKgKArVahVer1dWIkDOYlEJGYntEJEMwyAUCoFlWcGUSm6vk9AavEgMh8NCHqqaReJ+6HQ6WCwWWCyWbedHvV4Xzo9kMolisYh6vQ6j0bitEtmtrMhyuYxAIIBSqQSfz9c2w7F2ObQC3dk86zRELHaOdjqhislkMpKJxQ9/+MP48Ic/LMljE4hYVDVksdldOI7DxsYGaJqGwWCA1+tteTe6kxgMBtm1oSpBJO7HfiIyn89jY2MDq6urYFkWJpMJVqsVa2trKJVKim/X0xosyyIajSISicDpdBKn2n3Q6XQwm80YGho6VFYkLySlyoqsVCqgKAr5fB5erxcjIyMduwYdxKGV38xsdmhV21wkmVnsHPyGTbtJpVKkDVWhkDOPcGjUGOTeDvgZpVAohN7eXiwsLAjmB3LEaDTKprKoBpHYCpubm6BpGlarFWfOnIHD4di3EskvjomIlBfizEun04l7772XvDdHpJWsyEwmg3A4LGRF2my2LS2th82KrFarwqiA1+ttWz5xO2hVRPI/AyDEeihdRDYajSM5aRJap9FoSFZZJHmIyoTc0VRMJ7L5tLBzrtPpWgpd5jPwYrGYEJTeTUv8VjEYDKjVal17fvHO+G7xF2qAj0wIhULo6+vD0tLSFufbw7azEhHZHcQicXx8nIjEDnCUrEj+PNktK7JWqyEYDCKVSsHj8SjKVGovEcl/b9WhVfx4coK0oXYOqSqLUrahEqSF3NkIh4J3RNWCWDSZTIIZw07w8QYbGxuYmprChQsXFLVo7FZlsZWMRDUgNjoZGho6cPg6EZHygmEYRCIRxGIxTExMEJEoA1rJiiwUCkgmkyiXy+A4DlarFQ6HAxaLBblcDrlcDm63G36/X5Zi6TAcxFxH7EPA3w/kJCKJWOwce613joKUBjcEaSF3OBUj5aJba/EZ9Xp928WzUCiApmnk83m43W7Mzc0pcpHR6ZnFTsRfyAGxqJDC6OSoIpL/ToROazAMg3A4jHg8jomJCZw/f54sXmXOXlmRhUIBwWAQkUhEqDaGQiGsra1tM9dR2/u8m7nOXg6twLvdH3wbaydFJBGLnaNer8Nms7X9cUllUbmQVQLhUJjN5q62LnYScXwGx3HIZrOgKAoMw8Dr9WJxcVHRQqdTbqg7iUQliuv9qNfrCIfDSCaTXak8tSoiY7EYEZEtwLeXizNRyaJVuYhF/9TUFBYXF4XrEJ8VyVciw+HwjlmR/JfaOmuO6tAq5VwkEYudQ6oRo3Q6jZGRkbY/LkF6yGpAxZDKYnvgK4vJZBI0TcNisWB2dhZ9fX3dPrS2ILVYlENGYieoVqsIhULY2NjA9PS07EQFEZEHQywSp6amZPd+Eg6GeMZ0t8qwOCtSvKhtzoqMx+MoFApCu574HJFzVuRROIhDqxQiUqrsP8J2pJpZrFQqsNvtbX9cgvSQM49wKLQiFhmGETLAxsbGsLy8LEl7RjcRV07biVacTcvlMoLBILLZLFwul+JmnoiI3Iq4MixH0U84GOLcy8MaEe2WFQncNcYRz0QWi0XUajWYTKZtMR/dyoqUklZEJIAdRSSwdS5yr+smqSx2Dikqi+3IqyZ0D3Xc3Qk7InVlsVKpSPb43aZWqwmtShaLBW63Gx6Pp9uHJQntrixqRSQWi0XQNI1isQiPx4P5+XlVvU6tich6vS7MrE1PT+PChQuKEv2ErbAsi0QigWAwiLGxMclyL81mM8xm87YMXT4rslgsYmNjA8FgELVaDXq9flsl0mKxqOraAbTfoZWvThKkR4rKotjEjqA8lHEXJxwaPl+p3ai1slgul0HTNDKZDGZmZnDx4kUkEglVvlaedohFcbaX2kViPp8HRVGo1Wrwer0YGhpS5evcDbWJyHq9jmAwiPX1dczMzBCRqHA4jhNE4vDwMM6ePduVttBWsyIjkQgqlYqQFSk+Tw6bFSlnDuLQyv83fx2p1+uycmhVK1II883NTdWM7mgRedytCYpDbWJxc3MTFEWhUqnA4/FsCWI2Go0ol8tdPkLp0Ov1h95Q0EpGIgDB2AgAvF7vtkWg1lGaiKzVasKMKRGJyofjOKytrYGmaQwMDOD06dOyzLndLyuyWCzumRVpt9ths9lU91ndyVynVCphdXUVtVoNi4uLMBgMe1YjO+3QSmiddDqNoaGhbh8G4ZAQsahySGVxdziOQyqVAkVRMBgMggBoFjpSzfQpGa1kJHIch3Q6DYqiYDabMTs7uy3LjbA37RCR7XSeFIevu1wunD9/niwsFQzHcdjY2ABFUejt7cXJkydhsVi6fVgHppWsyGKxiLW1NZRKJSErUnye2Gw2Vcz1VatVUBSFzc1N+P3+Xbs3uu3QqkZ4p/J2Q8SisiFikXAolBydIZ5l6e3txcLCAhwOx65/n4jFd9FKRiLHcVhfXwdN07Db7VhYWCAubm2m0yKyVquBpmmk02lFGhERtsJv5AQCAdjtdiwvL8NqtXb7sNqOOCtSDMdxKJfLgrnOxsYGSqUSWJaFxWLZFvMhl7bvvWg0GqBpGhsbGy3NgXfboVWNNBoNSTYcUqkUyVhUMPK/ehCOhFSL+KO0LnaLRqOBSCSCaDSKkZERnD59uqUdaDVUUY+KVuIv+I2EUCiEgYEB1S5A5cx+IpJfHLcqIqvVqjCH7Ha7MTc3p7rNDa2RyWSwuroKi8WCxcVF1TlUtwLfnmqz2TA6Oir8XJwVWSwWEYlEUCqVJK/YHwWGYRCJRBCLxTAzM3Pkav9+IlL8dRSHVjUiVcZiJpMhlUUFQ8QiQfVUq1XBwGJychIXLlw40C6rFiqLOp0OLMtuuzFqxdmUYRjEYjFEIhGMjIzgzJkzqsxKUzJiESledOwmIuv1OhiGAcuyGB0dxfHjx2G321X5+dUK2WwWgUAARqMRx48f37MjRKvslRUprtjH43HhPOGzIsVCshPXP47jEI/HEQwGMT4+LnlMzW7Cr9mhVXzP28uhVY1CUqqMxXQ6TSqLCoaIRZUj9cJIqv72dlAoFEDTNPL5PFwuF2ZnZw91cdeCWOQdUfnfj1ZEIl9tjsfjcDqdktnrE6SjWURWKhXQNC3kXlqt1o7ORBLaz+bmJlZXV6HT6TA3N0fmhg/BbhV74N2sSD5TmM+KNBqNW84Ru92Onp6eI98L+DZ/iqIwNDTU9evuYRxagXeN3cTtrDs9jpKQsrI4Ozvb9scldAYiFgmHhhdRcltkZTIZUBQFhmHg8XiwuLh4pJubEltuD4rRaATDMDAajZoQieJMvampKRK8rgIqlQooikI+n4fb7d4y77RXO2s8HkehUCAiUoYUCgWsrq6CZVn4fL5tDqKE9tBKVmQqlUIoFEK1WhWyIsXnSqtZkZlMBisrK7Db7bI3I9rJoZWnlblI/jGUJCLr9bok17x0Or2l0k1QFkQsqhwpF/r8LJ8cFlPincqenh74/X6ysGgRfmc0n89v2SFVo0jkW5LT6TQJXlcJ5XIZFEWhUChsi73ZiVbbWYmI7B7FYhGrq6uo1+vw+/0kpqZL7JYVyTDMjlmROp1um7GOzWaDTqdDPp/HysoK9Ho9Tpw4oXjDMLWa6zQaDUnaUDOZDGlDVTBELBIOjdls7rrxC8uyiMViWwxJtGh2cBjEGYnj4+MIhUJbwqF5Bz6Hw9GW1qNuUi6XQdM0Njc34Xa7D92STJAPYpHo9XqxsLBwpM8oEZHdp1QqIRAIoFwuC5EJBPlhMBjQ19e3LWRdnBWZz+eFuUi+Gjk6Oorh4WFBQKnxGqx0EVmv1yVZQxGxqGyIWFQ5UlcWuxWfwbcRxuNxjI+P49y5c5IO5O9mAKNEdoq/GBkZERz1mneNw+EwqtUqDAbDtgB1s9ksaxHJz62Wy+WWqk4E+VMqlUBRFEqlEjwez5FF4n4cRUSKzxciInenUqkgEAigUCjA5/NheHiYnKcKRJwVyWclVqtVHDt2DFarVTDX2Skrkj9X1JIV2cxeIpL/LgeHVlJZJOwEEYuEQ9ONSAm+QpROpzEzM4OLFy925MbCz2cq2SGz1YzE3XaNG43GlkyvYDCIarUKk8kk3Oj5r24vjHO5HGiaRqPRgNfrxeDgIFl8KpxisQiKolAul+H1ersuKIiIPDri8PVOCH+C9NTrdQSDQWxsbMDr9W6ZHW5uPRVnRfJzkXxWZE9PzzZzHSVkRR6U/cx1Ou3QKsVoEcdxYBhG09c6paO+M4+whU7MLHaCfD6/pZrQ6QqRksViuzISjUYj+vv7t82C8iYIhUIByWRSmDUym81bqpAOh0PSmz3HcchkMqBpGnq9Hl6vl8ytqgBeJFYqFXi9XgwNDclaUBARuT+1Wk3Y9GsWFARlcpisxL2yIqvVqlCJjEaj25yM1X6uHMahld8EPopDq1SVRbWbBKodIhY1AH/xaDcmkwmVSqXtj8vDcRzS6TQoioJOp+tqhchkMikuPqNT8Re7mSDwmV47BaiLq5B2u/1I1WGO47CxsQGapmGxWHDs2DGSv6YCCoWC0Mbm8/kUXx0mInJr1cntdmNubk7R7ynh7ueX9w1oV1aiTqeDxWKBxWLZMStSfK7slBXJny8mk0l1ny+pHVqlqCzy2Y1qey+0BBGLhEMjVWWRZVkkk0nQNA2Hw4H5+fmu52oZjcaum/m0ilwyEs1mM4aGhrYtjKvVqnCzD4fDKBaLYFkWFotlSyXSbrfvuRvKcRySySRCoRAcDgcWFxeJuZEKKBQKCAQCqNfrQiVRzWhBRDYaDQSDQaytrcHlcrVUdSLIG96BPBAIYHh4uCNZibudK8DWrEjeGZ3Pimw2oVK6YdtutMNcp9FotP13k8lktsWyEJQFEYsaQKrKYrvdUBuNBqLRKCKRCEZGRnD69GnZZDDxbahyRi4icS/EO8bN2XeVSkWoRKZSKRSLRcEAodmZNZlMIhwOY3BwEPfcc49sPieEw5PP5xEIBNBoNIRKopZRg4hkGAahUAiJRIJE1aiIdDqN1dVV2O12nDp1ShbX372yIkulknBf2Skrkj9fWs2KVBqtiMharQaKorZlLbfDoTWdThNzG4VDxCLh0LSrslitVhEKhZBMJoWAdLntkstVLIrjL/j/lqNI3A+dTger1Qqr1bptdoW3Yt/c3ARFUSgWizAajRgYGIDZbMbm5iZYloXValXc6ya8KxIZhoHP5yOZevugBBEpnl+bnJxsS2siofvk83ncuXMHRqNRMVmJJpNpx1l7set3LpdDNBrdNSvSarWqcpNDr9eDYRhEo1HE43HBZIpfS7TLoTWVSqm+Q0TtELGoAaRaQB81OqNYLIKmaeRyObhcLtx3332yvSDLTSw2D7UDyhSJ+6HT6WA2m7G2tob19XWMj49jZmYGer1e2C3e3NxEPB5HuVwWbvRqyohUK5ubmwgEAuA4Dl6vl4jEI3IYEdlsQnVUEcmyrNAdMjExQUSiSiiVSoJxmd/vV4Vx2G6u3yzLCveWfD6PRCKBUqkEALDZbFvOFZvNJts1y37wYxwURW07V3ebZzysQyuJzVA+RCwSDo1erz9Ue2s2mwVFUajX6/B4PDhx4oTsF/MmkwnVarXbh9Fy/IUaqNVqCIVCWF9fx/T09LaFJy8GxfCh0IVCQciIrFQqMBgMWwx1lJARqVZyuRwCgQAAwOfzqWLhKWc6ISJZlkU8HkcoFILT6cS9996rypgDrSGONvH7/ZpY8Ov1+h3vLSzLCjEfhUJB0VmRmUwGKysr6O3txdmzZ1t2eT+MQyvDMHj55ZeJ6ZzC0e2z2CdetyqAYRjJqmKvvPIK7rvvvn3/Hj8MT9M0TCaT4ioJqVQK6+vrOH78eFeefzeRqEYqlQqCwSAymQxcLhfGx8ePvHsrzojk7dir1SqMRuM2Z1YlxqMoAV4k6nQ6+Hy+bTv6BHnAcRzq9fqWc0XsOCkWkTabDalUCsFgECMjI3C73bIbISAcnOasxLGxMdXeb45Kc1Yk/8UwzBbTNjlkRRaLRdy5cwc6nQ6zs7OSthFzHIcf/vCHuHr1Kk6fPo3PfvazmJ+fl+z5CG1h15OcbP0RjgwvXnaCZVnBVru/vx+Li4uKmHNoplttqO3KSFQCpVIJNE2jUCjA7Xbj2LFjbVugtJoRWSgUupIRqWay2SwCgQAMBgP8fj8R+AEQjAAAIABJREFUiTKHb/3eyclYLCIDgQCy2axQiWEYBslkUhbGOoTDwTAMwuEw4vF4y1mJWme/rEj+/tLNrMharYZAIIB8Po/Z2VnJzcPeeustXL58GVarFS+88ALm5uYkfT6C9JDKogZgWVay2Ief/OQnOH369LYLXb1eF246Y2NjcLlc6OnpkeQYOgG/I3fq1KmOPJ8SnE3bRT6fB03TqFar8Hg8GB4e7vprFWdE8tUVKTIi1Uwmk0EgEIDRaITP5+t6/A3h6PAdIhRFob+/H16vV3DFFp8rUs1EEqRB3EY8MTGBmZkZcl2TCHH7N//Fb1KaTKZtlcijjEuI3Yi9Xi+cTqek99b19XU8+eSTuHHjBp566ilcunSp6/dywoHY9c0iYlEDSCkWr127hmPHjgn5dpVKBTRNI5VKYXp6GlNTU6qoyNRqNbz55ps4d+6cpM+jJZHIz67yBidyj0po3inmF8aHyYhUM+l0GhRFwWQywefzkVkVFcBxHFKpFAKBABwOB3w+375xCTu1sxIRKS+asxI9Hg95H7qIuNOFF5L8uERzJXIv4zaO45BIJEDTNCYmJuByuSS9H1UqFTz33HP45je/icceewwPP/ywZu9/CoeIRS3D72RJwc2bNzE9PQ29Xg+KolAqleB2u+F0OlV1sWBZFq+//jouXrzY9scW21SrXSRyHId0Og2apmE0GuH1ehXflticEcnf5JszIpXunrcXHMcJlcSenh54vV4iElVCOp1GIBCA1WqF1+sVNgaPAl+5F2+8EBHZWcRZia2If0L34GfuxUJyt6xI3rlWXPmXCpZl8Q//8A/4yle+go985CP4zGc+A6vVKtnzESSHiEUtI5VY5DgOb775JorFIsxmM7xeL4aGhlQpcoDWzXxaRS0Zia3A72AHg0FYrVZ4PB7ViwlxRiS/IOYt2MWLYYfDodiMSF78UxQFi8UCr9eryJlkwnay2SxWV1dhNpvh8/k68r4SESk9m5ubWFlZgdFohN/vJ+erghFnRWazWaytrW3pdBG3tLYzK5LjOLz++uu4fPkylpeXcfXqVTidzrY8NqGrELGoZdotFvl8HpqmwbIsnE4n/H5/2x5frrRLLGolIxG4u/OYTCYRCoXQ19cHj8ej+Z1HcY4XvzDeKSPSbrfDYrHI8nPBtyVSFCVUnMiiUx3kcjmsrq4KhkRy2NQhIvLolEolrKysoNFoYHZ2VvEdHYS71Go1rK6uolAoYG5uDgMDA8I9RlyJbM6KFDsaH0RE0jSNy5cvo1wu48tf/jKWlpakemmEzkPEotap1WqHykQUwzAMotEowuEwhoeH4Xa7kUqlwDAM3G53m45UvhxVLO4UfwFAlmLgqPAuuJFIBMPDw4o3OOoE4oxI/otvNZJLRiTHcdjY2ABN07DZbG1rSyR0n3w+j9XVVXAcpxjXWiIi96darQpOmFrJStQCvHlNMplsOd5EnBUp/uI4bsvcvdVqhcFg2GJKls1m8cwzz+DHP/4xvvjFL+L973+/KtcuGoeIRa1zFLHIh6Mnk0nBKY2/8SaTScGOWe28+uqruHDhwoFbObRkWsMwDCKRCGKxmOCCq9VFWrsQZ0Ty3zudEcmLRIqi4HA44PF4iEhUCXwMRqPRgM/nU1T+7W40i8jdciLVLCJJVqI64TgO8XgcwWAQk5OTmJmZOXJ7qXjuvlgsIhQK4Q//8A9RqVQwNjaGvr4+3LhxAx/96EfxR3/0R1sidQiqgohFrVOv1wWx0ip87l02m4XL5cLk5OS2i1Imk0EikcDCwkI7D1eW/PSnP8XJkydbXpBrSSTyUSnJZBKTk5OqccGVM2LnPP4mX6vV2poRyc+a0jQNh8MBr9er+TZitVAqlRAIBFCpVOD3+2XvRtwOtCAim7MSd7pvE5RJOp3GysoK+vv74fP5JP2MsiyLl19+GV/5ylewsLCA48ePIxAI4NatW8jn83A6nThx4gQWFhbwm7/5m2TzUB3sukAlqznCNnK5HCiKQrVahdfrxcLCwq4ix2QySRbLITeMRqPQ4rQXWhKJ1WoVoVAIGxsbQogzyefqDCaTCQMDA9sqQeKMyHg8LrTmiTMi+UXxbu8Vx3FYW1tDMBhEb28vlpeXiUhUCeVyGYFAAKVSCT6fT9WmZM2YzWYMDQ1tq4yIRWQ8HlekiGzOSiTXYvVQKBRw584dGAwGLC0tSSrMeOPCz3/+85iamsKLL76ImZmZbX9nfX0dt27dwq1bt8hmhAYglUWN0Gg0wDDMrn8unkUyGo3weDwt7TRXq1XcuHEDZ8+ebefhypLr16/D7XbvOsujJZFYLpcRDAaRy+XgcrlUF5WiNlrNiLTb7UIbUn9/PzweD7HUVwmVSgUURSGfz8Pr9WJkZES116d2oYRKJL+xQ1EUyUpUGfy8qdi8RkpisRiuXr2KSCSCZ555BmfPniXXCG1B2lC1zm5iUbwb2dvbe2BXQynzB+XG7du34XQ6t+xKaykjEQCKxSJomkaxWITH48Ho6KhqX6sWEM+qJBIJpFIp6HQ6mEymbc6sas2IVDu1Wg0URSGbzcLj8ZDZtTYgFxHJZyXyLeJkY0cdMAyDYDCItbW1jsybFgoFfPWrX8V3v/tdXL58GQ8++CC51msT0oaqdZovNI1GA+FwGLFYDKOjozhz5syh3Cr1ev2RXVaVAt+GCmgrIxG4m81FURQajQY8Ho+mWtfUTjabRTAYxODgIC5evIienp5tGZHJZHJLRqRYSCo1I1Lt1Go1BINBpFIpuN1uHDt2jLxPbaLb7azirMQTJ06Q2BqVIDavmZqawvnz5yUVbY1GAy+88AKee+45PPLII3jttdckM0kjKBsiFjVGpVIRHNKmpqZw4cIFYkTSIvx8Ji8QtSASM5kMaJoGAHi9XlU4JRLuVsITiQRCoRCGhoZw+vTpLZtFfOaj3W7H2NjYln/Hx3vk83nE4/FtGZH8d7lmRKqder2OUCiEtbU1uN1u+P1+UiXoEFKLSJKVqF5SqRRWV1cxMDCAc+fOSVqR5jgOP/zhD/GFL3wBly5dwo9+9CPicErYE6ISNEKlUsHt27dRKBTgdrsxNzfX1gWEODdQjXAcB4PBgGQyCZ1Oh97eXlgsFlUuwvjAdZqmYTabMTs7uyVviaBcxCJxeHgYZ86cOdBOsjjzUYw4IzKbzSISiWzJiBRXIruVEal2+G6RRCKBmZmZQ8X8EKThqCLSaDQiHA6jUCjA7/eThb2KEJvXdMJI7Pbt27h8+TJsNhv+/u//XhOxZ4SjQ2YWNUKxWEQ2m8Xw8HDbF2o//elPcerUKVUO1YtNaxiGQSqVEgxCKpUK9Ho97HY7ent7tyyGlYjYAdNut8Pj8ZD2JpXAzyaHw2EMDw/D7XZ35HPKZ0SKjXWaMyL5BbFSz5tuI45KmJqawtTUFHHBVDi8iNzc3EQikUCpVILJZILNZpONsQ7haFSrVayurqJUKmFubg79/f2SPt/6+jqeeOIJ3LhxA08//TQuXbpENu0IzRCDG63DcRxqtZokj33t2jUcO3ZMVTk7rTqbMgwjLIL5r+asu97eXtjtdtm2+4qrTQMDA8QBU0WwLItYLIZwOIzR0VG43W5ZLC73yohsNtaRw/HKEZZlEYlEEI1GMTExgZmZGSISVcJuWYl7GeuQ80YZiM1rfD6f5CZx5XIZX/va1/DNb34Tjz32GB5++GHScUDYDSIWtY6UYvHmzZuYnp6WfGesE7Qr/kKcdcff1BuNBiwWiyAee3t7u+owyTAMYrEYIpEIRkdH4XK5SHVHJbAsi2g0ikgkgrGxMbhcLkUsHpsXw4fJiFQ74g2A8fFxzMzMyHYjinAwmrMSW90AICJS/nAch1gshlAohKmpKUxPT0t672dZFi+99BKeffZZfOQjH8FnPvMZkpVL2A8iFrWOlGLxnXfeweDgIEZHRyV5/E7QiYxEcUwB/1UqlcBxHGw22xYRKaU5SKPRQCQSQTwex/j4OKanp8kCQiWINwCcTidmZmYU/97ulxHZvBhW6665uAOA39xR+ntLuIs4K3FkZKRtHQBERMqDVCqFlZUVDA0NSZ6DyXEcXnvtNVy5cgXLy8u4evUqnE6nZM+3E+FwGB/72MeQSCSg1+vxO7/zO/iDP/iDjh4D4VAQsUi4e+OQIuaCoij09PRgcnKy7Y8tJXKJvxA7TEo5D1mr1RAOh7G2tkZmm1QGwzCIRqOIRqNwOp1wuVyqrzaJN1/Ei2GO42C1WlWTEclxHJLJJGia7ui8KaEziLMSfT7foSKsDspOIrLRaOyYr0pE5OEpFAp45513YDKZMDs7K3llj6IoXLlyBZVKBV/60pewtLQk6fPtRjweRzwex5kzZ5DP53H27Fn80z/9E06cONGV4yG0DBGLBOnEYiQSAcMwcLvdbX9sKeBjL1iWlXX8RbvmISuVCkKhENLpNGZmZjAxMaHYhTNhKwzDIBKJIBaLkZbE/wHHcSiXy9sq+ICyMiI5jsP6+jooihJmiTshJAidQZyVODs7K4uZ/1Yqkfx3IiJ3p9PmNdlsFs888wx+/OMf44tf/CLe//73y+q69uCDD+L3fu/38L73va/bh0LYGyIWCXdNJfg2y3aytraGzc1N2VswiwWiOOpDThfVVmh1HhIAQqEQ8vk83G43nE6n4l4rYWfEInFiYgLT09OaF4n7wVfwxe2scsyI5DgOGxsboCgKvb298Hq9xHBKRRSLRayurioqK5GIyNZoNBoIBoNYX1/viHlNrVbD17/+dTz//PP41Kc+hU984hOyuw/QNI33vOc9uHHjhiI+6xqHiEWCdGIxk8kgkUhgYWGh7Y/dDnYSiWoTTeKWvHQ6jbW1NeFm3tfX17F5SIK0iOdNJycnMT09TVqJj4g4I1Ic78G3gfNVSKkzIjmOQzqdRiAQgM1mg8/nI4YUKqJSqYCiKFVlJYpFJC8ktSgixeY109PTmJqakty85jvf+Q6eeuopPPDAA3jsscdkmYVcKBTw3ve+F5///OfxG7/xG90+HML+ELFIuLvQZBim7Y9bKBQQCARwzz33tP2xj0InTGvkRC6XA0VRYFkWHo8Hg4OD4DiuI/OQBGkRB64TkdgZ+DbwTmREZjIZrK6uwmKxwOfzyaIlkdAe6vU6aJpGKpXqSLVJDmhJRG5sbGB1dbVj5jVvvPEGHn/8cUxPT+OJJ57AzMyMZM93FOr1Oj74wQ/i137t1/DZz36224dDaA0iFgnSicVqtYrr16/j3LlzbX/sw6AlkchxHDKZDGiahl6vh9frbWk+Qg35kFqg0WggFAohmUwSUyKZ0M6MyFwuh9XVVRiNRvh8Pjgcjg69CoLUiLMSXS4XmRWHukRkPp/HnTt3YDab4ff7Je8CiMViuHr1KqLRKJ555hmcOXNGtusajuPw8Y9/HENDQ/jqV7/a7cMhtA4Ri4S7N69Go9H2x2VZFq+//jouXrzY9sc+CFoTiRsbG6BpGlarFR6Ppy0LTSXkQ2qBer2OcDiMZDKJ6elpTE5OEpEocw6SEcnPrel0Ovj9flm2kBEOhzgH8yBZiVpGSSKyUqlgdXUVlUoFc3Nzks/hFQoFfPWrX8V3vvMdXLlyBQ8++KDs773//u//jkuXLmF5eVk41ieffBIPPPBAl4+MsA9ELBKkE4sA8Morr+C+++6T5LH3gv/8akkkJpNJBINB9Pb2wuPxSN6yJpd8SC1Qr9cRCoWwtrbWkdkXgrTw+bb8eZPNZpHJZMCyLHp7ezEwMCAISZvNRkSFgpEqK1HLyElENhoN0DSNjY0N+P1+jIyMSHqvazQaeOGFF/Dcc8/hkUcewaOPPkpGRQhSQ8Qi4a6gqtfrkjx2p8WiXDISOwXLsojH4wiHwxgcHITb7e66Q2Kn8iG1QL1eF1z0ZmZmMDk5SUSiiigWiwgEAqjVavD7/ejv79dERqRWSKVSWF1dRW9vb8eyErVMJ0WkuFLciQ08juPwgx/8AFevXsWlS5fw+OOPq8IMiaAIiFgkSC8WL168KLlYU0pGYrsQh62PjY1hZmZG9sKLzEO2Tq1WQzAYRCqVIhmYKqRcLiMQCKBUKrXkgLlXRqTNZtvizCrnjEitwGclmkwm+P1+YkzUZdopIvlRj0AggOHhYXg8HsnvV7dv38bly5dht9vx1FNPyT6OjKA6iFgkvNsSJQU//elPcerUKclaQdSSkdgq9XodkUgEiURCNTl6ZB7yXcQi0eVyYXx8XPWvWUtUKhUEAgEUCgX4fD4MDw8f6VqllIxIraDErEQtc1ARmc/n8c4776Cnpwezs7OSd/Gsra3hySefxM2bN/H000/j/vvvJ+cwoRsQsUiQVixeu3YNc3NzsNvtbX1cLZnWAHdvaqFQCOvr65owNtHaPGS1WkUwGEQ6nSYiUYVUq1VQFIVcLgev1yt5TEJzRmSxWNzSCt6pjEitwG8CFItF1WQlaplarbalDXxzcxPFYhEAMDw8jKGhIUlnIsvlMr72ta/hxRdfxOc+9zk8/PDD5H5A6CZELBKkFYs3b97E1NQUBgYG2vJ4WhOJlUoFwWAQmUyGiAiobx6yWq2CpmlkMhm43W6Mj4+r+vOsNWq1GmiaRjqdhsfjgdPp7Or728mMSC2gxaxELdFsXtPX1yfcf6SYiWRZFi+99BKeffZZPPTQQ/j0pz8tefQGgdACRCwS7lKtViV53HfeeQeDg4MYHR090uNoTSQWi0XQNI1isQi3242xsTFVv96jorR5SPEmgBxEBKG98MZEGxsbitgEaGdGpBYgWYnqhmVZRKNRRCKRlozFmiuRBxWRHMfhtddew5UrV7C8vIyrV6/C6XRK+RIJhINAxCLhLrVaDfu854eCoij09PRgcnLyUP9eayIxn8+DoijUajV4PJ4jzzRpHbnNQ1YqFdA0jVwuB4/HQzYBVEaj0UAoFEIymVSFiDhIRqSa2+J5xA6Yk5OTmJ6e1sTr1gq8ec3q6ipGRkaObF6zk4iMRqP4sz/7M8zNzeHEiROYnJzEt7/9bbAsiy996UtYWlpq4ysiENoCEYuEu9TrdUGQtZNIJAKGYeB2u1v+N1rLSASAbDYLiqIAAB6PB4ODg10+IvXSjXnIcrkMmqaxublJRKIKEVea1J6D2ZwRyS+EGYaBxWLZMg+ploxIkpWofjY3N3Hnzh1YLBb4/X5JzWvi8TheeeUVfOtb38KdO3cEQTo8PIzFxUWcOHECi4uLWFxcJPOvBDlAxCLhLlKJxbW1NWxubrZk9ay1jESO45BOp0HTNIxGI7xeL3HP6yJSzEOWy2VQFIVCoQCPx0NmmlQGwzCIRCKIxWKarzSJN2HUlBHJZyX29fXB6/WSrESVUalUsLKyglqthrm5OfT29kr6fLVaDd/4xjfwt3/7t/jUpz6FT3ziE4JY3NjYwK1bt3Dz5k3h+1/91V/h2LFjkh4TgbAPRCwS7tJoNMAwTNsfN5PJIJFIYGFhYde/0xx/AahfJK6vr4Omadjtdng8nra7xRLax2HmIUulEmiaRqFQgNfrxcjIiGo/z1pEPNM0Pj4Ol8ulWZG4H80ZkXxMAbA1I5IXkXI5T3K5HFZWVmA2m0lWogppNBqgKArpdBp+v1/ykQ+WZfHyyy/j6aefxgMPPIA//uM/hsPhkOz5CIQ2QsQi4S5SicVCoYDV1VWcPHly259pLSORZVkkk0mEQiH09/fD7XYTpzMFs1MrXr1eR6PRAACMj49jYmICdrtdMVUUwt6wLIt4PI5QKISxsTG43W5ZGCYpEblmRPJZiQzDYHZ2VvJKE6GzHNS85qhwHIdr167h8uXLmJ6exhNPPIGZmRnJno9AkAAiFgl3kUosVqtVXL9+HefOnRN+pjXTGoZhEI/HEQ6HMTIyApfLRVqZVEaxWARFUSiVSpienobJZNJEPqRW4DgOiUQCwWCQzKxJTKsZkXa7HT09PW07h0hWorrhO3oCgQBGR0c7stETjUZx9epVxGIxPPPMMzhz5gy55hOUCBGLhLswDCNURNoJy7J4/fXXcfHiRc2JxEajgWg0ilgsBqfTiZmZGbLAVBm8SKxUKvB6vRgaGtrxM622fEitIDY2GRoagsfjIe9Pl9gvI1IsJA/yHpGsRPXDtxR3wrwGuNtR9eyzz+J73/serly5gg996EOku4SgZIhYJNyFZVnU63VJHvuVV17BhQsXNCMS6/U6QqEQ1tbWMDk5iampKdKqpjIKhQIoikK1WoXP58Pg4OChPtNKy4fUCuK5YmJsIm/EGZH891YyIhmGQSgUQiKRgNvtxsTEhKrvS1qkXC5jZWUF9Xq9I+Y1jUYDL7zwAp577jk88sgjePTRR8nmEkENELFIuIsUYpGvJL755psolUqCIx5fRbFaraq6OVerVYRCIaRSKUxPT0s+C0HoPIVCAYFAAPV6XagkSoHc8iG1AsdxSKVSoCgKdrsdPp9P8ioEQRp2y4jkF+/FYhFOpxNer5cs6FUGXy3mzWtGRkYkfT6O4/CDH/wAV69exaVLl/D444+TNmaCmiBikXCXdonF3eIvgLu7fPl8fouZgV6v35LL1dvbq7hWTXGGnsvlgtPpJAt4lZHP5xEIBNBoNIRKYqfpRj6klkin0wgEArBYLPD5fMT9UmXwc6cURQnnCn8+qTkjUkuwLItIJIJoNAqXy4XJyUnJr4O3b9/G448/DofDgaeeeqqlmDACQWEQsUi4Cx+0fJR/L3Y3BVprN21uw8vn86jX6+jp6dkyxyVHR0l+Xq1cLsPtdpNZFxXCi0SGYeDz+TAwMNDtQ9oGmYc8GtlsFqurqzCZTPD7/STGRoXsl5XIb8SIq5DNGZF8Syup5suPZvMaj8cjudBfW1vDE088gVu3buHpp5/G/fffT+7/BLVCxCLhLocVi1LEX/DHIq5C8jdu8QxKb29vW93wWmVzcxMURaHRaMDj8exqakJQLpubmwgEAuA4Dl6vV5YicT/IPOTebG5uYnV1FXq9Hn6/n2SeqZCjZiWKMyLFc5GAvDMitUQul8OdO3dgs9ng9/slny0ul8t47rnn8NJLL+Fzn/scHn744Y5uHvzWb/0W/vmf/xljY2O4ceNGx56XoGmIWCS8S7Vabfnv7iQSpb5RNldQ8vk8qtUqDAbDlllIh8MhyeI3k8mAoijodDrFCgjC3uRyOQQCAQCAz+dDf39/l4+o/Wh9HjKfz2N1dRUcx8Hv96Ovr6/bh0RoM8ViESsrK2BZVpKsxP0yIsWbmqQlXBp485pGo4G5uTnJN3tYlsVLL72EZ599Fg899BA+/elPdyUn+V//9V/hcDjwsY99jIhFQqcgYpHwLrVaDfu877KMv+Dd8MSVyN1mUA66+OUNL2iaRk9PDzweDwlpViHZbFbYCPD5fJoTEFqYh+TNifi5U7LZoz7EWYmzs7Mdny1mWXabM2snMiK1RL1eB0VRyGQymJ2dxfDwsKTPx3EcXnvtNVy5cgXLy8u4evUqnE6npM+5HzRN44Mf/CARi4ROQcQi4V32EotyFIl70bz4zefzKJVKws6vuAq5U9sKn68WDAbhcDjgdrvJLJMKyWazCAQCMBgM8Hq9mhOJ+6GGechSqYRAIIBKpQKfz0dcClWI3LMSGYbZUoVsV0aklhCb13Qq6oSiKFy5cgWVSgVf/vKXsbi4KOnztQoRi4QOQ8Qi4V3q9bogBnmUJhL3g9/5FVcha7UaTCaTcNOuVqtYW1vD0NAQ3G43sc5XIZlMBoFAAEajET6fj1SLD4gS5iHL5TIoikKxWBREopKvXYTtKD0rcbeMSP5+tFtGpJbgN24pisLY2Bjcbrfk5jWZTAZf/vKX8eqrr+JP//RP8b73vU9WnysiFgkdhohFwrvwYpF/79UkEvejXC4jGAwimUzCbDYLr1Xt2ZBaI51Og6IomEwm+Hw+YmrSZuQwD1mpVIQoG6/Xi5GREXLOqgyWZRGLxRAOhzE5OYnp6WlVxVzUarVtlchGo4Genp5t7axqNqfqtHlNrVbD17/+dTz//PP41Kc+hU984hOy/P0SsUjoMLveQOV3dhA6Asdx2zIS1bzQajQaCIfDSCQSGB8fx3333Sfs4HIcJ7Tg5fN5xONx1WRDagmO44RKYk9PD+bn54lIlAiz2YyhoaEtrZ7NLeEbGxuSzEPWajVQFIVsNguPx4P5+XlVX7u0CMdxSCaToGkao6OjuPfee2W5mD8qZrMZZrN5y8wl7xLOb8JEo1HVZkSWSiWsrKyAYRgcP368I+Y1L7/8Mp5++ml84AMfwKuvvkruEQRCC5DKogZ55JFHYLPZsLS0hKWlJRw/fly1Q/i1Wg2hUAjr6+uYmprC1NRUyzdXcQse386qlGxILcFxnFBJtFgs8Hq9ZO5URrRrHlI8r+Z2uzE+Pq7Ka5aW4c/lvbIStcp+GZHiSqTcHY7r9ToCgQByuRz8fn9HzGuuXbuGy5cvY3p6Gk8++SSmp6clfc6j8vDDD+OHP/whNjY24HQ6cfXqVfz2b/92tw+LoG5IGyrhXaLRKN588028+eabuH79Ot566y0wDIPZ2VlBQC4vL2NyclLWN5y9qFQqCAaDyGQymJmZwcTERFtei9yzIbUE72BLURSsVisRiQqj1XlIs9mMWCyG9fV1uFwujI+PK/a6RNido2YlapWdMiLFFX05ZUSyLItwOIxYLNax2dNoNIqrV68iFovhmWeewZkzZ8h9mUDYGSIWCXtTq9Xw1ltv4Y033hBEZDQaxcDAAJaWlrC4uIilpSWcOHECdrtdthfbUqkEmqaRz+fhdrvhdDo7cqzi6gkvJPlsSHHlRKpsSC3BcRw2NjZA0zRsNhu8Xi9ZWKoIvgVvc3MTyWQShUIBJpMJvb29msiH1BpSZyVqFZZlBRHZ7YxIsXmN0+mEy+WSvH02n8/j2Wefxb/8y7/gypUr+NCHPkSuFwTC3hCxSDg4fEvQm28dk8kXAAAgAElEQVS+iTfeeAPXr1/HzZs3US6X4fF4BAG5tLQEr9fb1dmJQqEAiqJQqVTg8XhkY3ZRr9e3VU8ajYZgqMNXIa1WK7mR7QMvEimKgsPhgNfr7UpYMkFaGIZBJBJBLBYTWsf1er3q8yG1RrezErVKpzMis9ks7ty5A4fDAZ/PJ3lbcaPRwN/93d/ha1/7Gh555BE8+uijJKaEQGgNIhYJ7YNhGKysrGypQtI0DYvFgsXFxS0icmBgQNKFWy6XA0VRYFkWHo8Hg4ODsl8oHjUbUmtwHIf19XXQNE1EoooR56tNTExgZmZm3w0oNeRDag1x2LrX65VdVqJW2SsjUiwiWz2XSqUS7ty5A5ZlMTc3J7mRDMdx+MEPfoCrV6/iPe95Dx5//HGyAUEgHAwiFgnSwnEc8vk8rl+/vmUeMpfLYWpqSmhlXV5extzc3JFcRXnXS4qiYDQa4fF40N/f38ZX0x0YhkGpVNoyD1mtVoUZLr4KabfbFe2A1yp86xJN0+jr64PH4yEiUYWI4xH4FrWjtmorIR9Sayg9K1GrHDQjUmxeMzs7u8UxWSpu3bqFy5cvw+Fw4KmnnsLs7Kzkz0kgqBAiFgndgWVZhEIhoZX1zTffxMrKCgwGA+bn54UK5NLSEsbGxvZcPIhn1axWKzwejyZsr8WZdvl8HsViESzLwmq1bqmcqCUbUiwS+/v74fF4YLFYun1YhDbDcRzi8ThCoRBGRkbgdrslj6aRQz6k1mBZFtFoFJFIBJOTk5iZmSG/WxWwU0ZkqVQCwzAYGBiA0+mUPCNybW0NTzzxBG7fvo2nnnoK999/vyrugQRClyBikSAfePe227dvb2llXVtbw+joqNDKury8jOPHj8NoNOL555/HX//1X+Mv/uIvcM8992i+wiTOhhSbFyg5G5LPVgsGgxgYGIDb7SYiUYWIM/SGh4fhdru72iLa3BZO5iHbQ3NWotvtJlVcFcK/z7x5zfj4OMrl8hYh2ZwRyRvsHLZDplwu47nnnsNLL72Exx57DA899BDZgCAQjg4RiwT5w3EcEomEUIW8du0aXnnlFRQKBSwsLODixYs4f/48lpeXBdMLwlb49jtxK6vcsyH59z0YDGJwcBAej4fMaqoQfvaUoigMDAzI/n0m85CHozkr0efzkd+PSslkMlhZWUFvb++e7zPHcahWq9s2ZPgOmVYzIlmWxYsvvohnn30WDz/8MD796U9rfuOYQGgjRCwSlEOpVMLf/M3f4Bvf+AY+/OEP43d/93exsbGxpQoZDofR19e3JdZjcXERDoeD7Pw3sdONWg7ZkCzLIpFIIBQKYWhoCG63W9bigXA4xC62vb298Hq9iq4Yk3nI3eGzEnt6euD3+8lCXqXwcSccx2Fubu7Q+bZ7ZUR++9vfBsMwWF5exj333IPNzU38yZ/8CZaXl3H16lU4nc42vyoCQfMQsUhQBteuXcPHP/5xfPSjH8UnP/nJXTO3eJOb5liPYrG4LdbD5/NpwhDmoOyUDVmpVGA0GiXNhhSLRDm0IRKkga8wBQIB2Gw2+Hw+VYsHLc9DkqxEbVCr1RAIBLC5uYm5uTnJ3EZZlsWtW7fws5/9DD/72c/w85//HOFwGJOTkzh16tSWTWKXy6W684lA6BJELBKUQa1WA8uyh648MAzz/7d358FR1vcfwN8bcm/um2RJNrsJ5FQIggoKTBWrHShjS9XijFIGhR5OsKMcDUegxiRoEUdRRlFBbJ3i1algUcSxl5SWGklCDrK7SUhCLkKO3c0mezzP7w9/u91NABPI3u/XDKOuMM83S47n83y+388bGo3GoYjUaDQICQlBXl6e7Sxkfn4+4uLi2IW8gitlQ9qfObEWkpPNhhQEAZ2dnWhra0NCQgLS09NZJPqo/v5+29ddZmbmdXcevJ2vn4ccGRmBWq3G8PAwsxJ9mMViQVtbGzo7OyGXy5GSkuL0z9X+/n7s3r0bp06dwjPPPIOlS5fCaDSisbER586dQ21tLc6dO4fW1lbcfvvteOWVV5y6HiI/wGKR/JcoitDpdKitrXXYyjowMIDU1NRxsR4sYMazv+m1diGt2ZD2HcgrZUPaRyNYB114y9AdmpzBwUGo1WoEBgZCoVD4xbTi6+Ht5yHtsxIVCgUSEhK8rtCl72Y9T97S0jLh7NMbZTQa8cYbb+DgwYMoLi7G6tWrv3Nni8Vi4e4hohvHYpFoLGsIuH2sR1NTEyQSCWbOnGnbxlpYWIikpCRudbmCqwU5BwcHQyqVwmQyYXBwEMnJyZDL5SwSfZRWq4VKpYJEIoFSqeQ2xOvk6echmZXoP/r7+9HU1OSyIUWCIODYsWOoqKjAsmXLsGnTJj5sInItFotEE2HtoF0p1iM+Pt7hLGRubq5Xbh1zNusNZXt7uy2o2WAw+HQ2pL/S6XRQq9WwWCxQKpWIjo5295J8krvPQ9pnJaalpUEmk/HhmY/S6/W2h6ZZWVlO30IuiiK++eYbbNu2DTKZDM8++yxkMplTr0lEV8RikehGWIPi7buQ9fX1MJlMUCqVPHCPb4vEjo4OdHR0IDk5Genp6Q7dj4lkQ1oLSXYgPZter4dGo4HRaIRSqURMTIy7l+R3XHEeklmJ/sM6vEar1brs/GlHRwdKS0vR1dWF3bt3o6ioiA8PidyHxSKRM5hMJpw/f35crEdERMS4WI/IyEif/EFosVjQ3t6OixcvIiUlBTNmzJjUDaXZbIZer/eqbEh/ZTAYoNFoMDw8DKVSibi4OHcvicaYivOQoiiir68PGo0G0dHRyMzM9Mizk3TjrDtBuru7IZfLkZyc7PSfU1qtFi+88AI+++wz7NixA8uXL+f3diL3Y7FI5CqiKGJgYADV1dW2ArK2thY6nQ7p6ekOE1mVSqXXPqm3n5A3ffp0yGSyKftYPDUb0l+NjIygubkZWq0WCoUC8fHxfM+9zETPQ1osFjQ3NzMr0ceNHV7jih0xZrMZ77zzDl599VU89thjWL9+PR9CEHkOFotE7ma9CRsb6xEUFDQu1sOTb8bNZjPa29vR2dmJ1NRUyGQyl02is3ZN7LuQrsiG9Fejo6NoaWnBwMAAMjMzkZiY6LGfl3R9rOch+/r60NXVBbPZjODg4HFbWX0xH9JfXb58GSqVymVdY1EU8cUXX2Dnzp1YvHgxtm7dypgVIs/DYpHIE4miCL1ej3PnzjlsZb18+TKmT5+O/Px8WxE5c+ZMBAcHu+1m3Ww2o62tDV1dXS4vEr+LfTakVqu1DQAJCwtzOAsZHh7OYmcCjEYjWlpacPnyZZdtTSP3sGYlGgwGKJVKxMbG+nw+pL+yH16TnZ2N8PBwp1+zrq4O27ZtQ0REBMrLy5GVleX0axLRdWGxSORNrNmEZ8+etXUhz58/D1EUx8V6JCcnO/WJv8lkQltbG7q7u5GWloa0tDSPKRKvxXrDa9+FvFI2ZGRkJLdC/T+TyYTW1lZcunQJ6enpjEbwYdYHApPJSrzWecixeav8mvIcRqMRarUaOp0O2dnZLhlI1d3djbKyMjQ2NqK8vBwLFy7k9xIiz8ZikTxPW1sbHnnkEXR1dSEgIACPP/44iouL3b0sjyWKIoxG47hYj87OTsTFxY2L9bjRLprJZMKFCxfQ09MDmUyG1NRUrygSv8vYbEitVutwdsvahZRKpT7x8U6E2Wy2DbmwFonccuibLBYLWltb0d3dPWVZiZ6eD+mv7IfXZGZmIikpyekFm8FgwL59+/DBBx9g06ZNeOihh9z2veT48eMoLi6GxWLB2rVrsXnzZresg8hLsFgkz9PZ2YnOzk4UFRVBq9Vi7ty5+NOf/oS8vDx3L82riKKI3t5eh1iPhoYGjI6OQqFQOExlzcjI+M4f3GOLxLS0NL8oHKxnt6ydSL1eD0EQEB4e7tAx8aVsSPshRf70d+2P3JGV6O58SH8liiI6OzvR2tqK1NRUzJgxw+nvryAIeO+99/DCCy9g1apV2LBhA0JDQ516zWuxWCyYOXMmTpw4AZlMhnnz5uHdd9/l/QXR1bFYJM+3YsUK/OpXv8LSpUvdvRSfYDab0dTU5NCFbG1thVQqtZ2FtHYio6Ki0NPTg/LychgMBmzbtg2pqal+fwM3NhtSq9WO23bnjdmQ9pmYnnb+lKaWdepla2urR2QlXus8pP2k44iICJ6HvA72w2sUCoXTvy+JoohTp05h+/btuPnmm7Fz504kJSU59ZoTcerUKZSWluLTTz8FAJSXlwMAtmzZ4s5lEXmyq36z5X4Q8ggtLS2oqqrCrbfe6u6l+IzAwEDk5uYiNzcXDz30EIBvf7APDg7aYj3ef/99lJSUoLW1FcHBwbj99ttx3333QafTQRAEvy8WJRIJpFIppFIpkpOTba/bZ0N2d3dDrVZ7RTakfXcpJSUF8+bN47ZAHzU2K7GoqMgjzhFKJBKEhYUhLCwMiYmJttftz0MODg6io6OD5yEnQafToampCdOmTUNBQYFLhteo1Wrs2LEDRqMRr7/+OvLz851+zYnq6OjAjBkzbP8tk8lw+vRpN66IyHvxLoHcTqfT4cc//jH27t2LqKgody/Hp0kkEsTExGDRokXIzc1FW1sbzGYzKioqsGDBAtt5yGPHjkGlUiEoKAg5OTm2iawFBQUTGoTh6wIDAxEdHY3o6Gjba2OzIfv6+qDX6wHAtpXVWki6OhtSEAR0dnbiwoULSEpKwi233OJVnVCanIGBAajVaoSEhKCwsNArshLti0J79uche3t70dzczPOQdkZHR6FWq6HX6102vKa/vx+VlZU4ffo0fvvb32Lp0qUe9zPhSrvmPG2NRN6C21DJrUwmE5YtW4bvf//7+PWvf+3u5fiNffv24Y033sCTTz6Jn/70p1e8ybJuwRwb69HX14eUlBSHWI9Zs2a5NdbDk10tGzIoKGhcx2Sqb3bttyAmJCQgIyODRaIP0+l0UKlUAICsrKxxhZcv8ffzkNZBRT09PS4bXmM0GnHgwAEcOnQIxcXFWL16tccW6NyGSjRpPLNInkcURTz66KOIi4vD3r173b0cv9Le3o7p06df1zk1QRDQ1dXlEOvR0NAAQRCQnZ3tEOvBqZpX58xsSFEU0dPTg5aWFsTGxkIul3Prng8zGAzQaDQwGAzIyspySXfJE/nDeUj74TWuGlQkCAKOHTuGiooKLF++HBs3bvT4BxFmsxkzZ87EyZMnkZaWhnnz5uEPf/iDR22VJfIwLBbJ8/zjH//AnXfeicLCQtsPu2effRY/+MEP3LwymixRFGEyma4Y6xETE+MwTCcvL++GYz181Y1mQ4qiiEuXLqG5uRlRUVGQy+VunUhIzmU0GtHc3IyBgYEJZyX6I1/Jh+zr64NarUZMTAwyMzNdMrymqqoK27ZtQ3p6OsrKyiCTyZx6zan0ySefYMOGDbBYLFizZg1KSkom9OdEUcSdd96JkpIS3HfffQCAI0eO4M0338Tx48eduWQid2KxSESuZx2yYR/rUVdXh5GREWRmZjrEesjlck7kvAr7bEhrIWl/bisiIsJ2LjEiIgKZmZlecU6Nro99LqZcLkdKSgqLxOvgLfmQ9sNrsrOzXfK13dHRgdLSUnR1dWH37t0oKiryq8+x2tpa/OQnP0FVVRUsFgtmz56N48ePQ6lUuntpRM7CYpGIPIfZbIZKpRoX6xEWFjYu1iM6OtqvblImw2g04uLFi2hvbwcATJs2DRKJxCEbMjIy0mu33JEjd2Ql+iNPOQ9pHV4zPDyM7Oxsh4FazqLVarFnzx6cOHECO3bswPLly/32c2zjxo2QSqXQ6/WIjIzEtm3b3L0kImdisUhEnk0URQwNDaGmpsYW7VFTU4OhoSHIZDKHLmR2drbfD2qxTrwMCgqCUqmEVCoF4JgNae1C2m+5s4/28Pf30Ft4WlaiP3LleUiLxYKWlhb09vZCoVAgMTHR6Q97zGYzDh8+jP379+Oxxx7D+vXrPXpLrivo9Xpb5MyZM2cQEhLi7iUROROLRSLyToIgoLW11baVtaamBiqVCoGBgZg1a5ZtImt+fr5LJgK629DQENRqNQICAqBQKBAZGTmhP2c2m8dtuTOZTAgNDXW40fW0bEh/NjYrMTMz0+9v4D3NVJ6HFEURFy9exIULF1zWORZFEV988QV27tyJJUuWoKSkBLGxsU69pjfZvn07IiIisHHjRncvhcjZWCwSke8QRREGgwF1dXUOW1l7enqQnJzsEOuRk5Pj8lxDZ9BqtdBoNBAEAUqlckoyScdmQ2q12nHdEndlQ/q7gYEBqFQqhIaGQqlU8gyql5nseci+vj6oVCrExcVBLpe7pOtfV1eHrVu3IioqCuXl5TyPdwWlpaWIiIjAU0895e6lEDkbi0Ui8n3W7XpjYz0sFguysrJs5yALCgqQlpbmFR00vV4PtVoNs9kMhULhklgEd2ZD+jt/ykr0R2PPQw4NDWF4eBiBgYFITExETEyM089Ddnd3o6ysDA0NDaioqMDChQv5IOgqWCySH2GxSET+y2g0orGx0aEL2d7ejujoaIezkPn5+ZBKpR5x4zQ8PAyNRoORkREoFArExcW5e0lOzYb0d8xK9C8jIyNQq9W2v++QkBCnn4c0GAzYt28fPvjgA2zatAkPPfSQVzwwcycWi+RHWCwSEdkTRRGXL192OAtZV1eH4eFhyOVyhwJSoVC4LNbDYDCgubkZer3eViR6cuF1tWzIgIAAhxvdq2VD+jtmJfoXs9mM1tbWCQ2vmarzkIIg4MiRI9i7dy9WrVqFDRs2MH+ViMZisUjkj0ZGRrBo0SKMjo7CbDZj5cqV2Llzp7uX5dEsFgvUarVDF7K5uRmhoaHIy8tziPWIjY2dshv7kZERtLS0YGhoCJmZmV5fNHxXNqS1CymVSv0yX9OaldjT04OMjAxmJfo4URTR0dGBtrY2yGSyG9oGf63zkO+++y7S0tIwe/ZszJ49G/X19di+fTtuvvlm7Ny5E0lJSVP8kRGRj2CxSOSPRFGEXq9HREQETCYT7rjjDrz44ou47bbb3L00ryKKIrRarUOsR21tLQYGBpCWljYu1mMyHTT7zpJcLvf5ia5Go9GhC6nX6yEIgt9kQwqCgPb2dnR0dDAr0Q9YJ9qq1WqnD68xGo34/PPPcfbsWVRVVaGhoQGXLl3CnDlzsGDBAhQUFKCwsBAzZ85kl5+IxmKxSOTvhoeHcccdd+DVV1/Frbfe6u7l+ARBENDW1mbbylpdXY2mpiYEBARg1qxZDgN1kpOTHYqfnp4eHDx4EIsWLfL7zpI/ZEPaZyUmJSUhPT2dw4F8nFarRVNTE4KDg1020ba/vx+VlZU4ffo0nnnmGdx1111ob29HTU0NampqUFtbi8bGRgiCgAcffJCREERkxWKRyF9ZLBbMnTsXKpUKv/zlL1FZWenuJfk06xk++1iP2tpa9PT0ICEhAdnZ2ejp6UF1dTXWrFmDJ554gkXDVUwkG9LZkyNvlCiKuHTpEjQaDWJiYpiV6Aesw2tGRkaQnZ09JTE338VoNOLAgQM4dOgQiouLsXr16mt+XzGZTBgcHERCQoLT10ZEXoHFIpG/GxgYwP3334+XXnoJBQUF7l6O39HpdCgvL8e7776LuXPnIjg4GOfPn4fJZIJSqbR1IAsLC7k18RrssyGtXcjh4WEAQHh4uEMX0t3ZkNasxLCwMCgUCmYl+jiz2YyWlhZcunQJSqXSJeeOBUHA0aNHUVlZieXLl2Pjxo2MWyGi63HVb1Z8nE3kJ2JiYrBkyRIcP36cxaILGQwG7N+/HwcPHsSaNWtQV1fnMInQZDLZYj3OnDmDgwcPoq2tDZGRkbazkNZfkZGRfrtV1UoikSA0NBShoaEOXRFBEGwDdfr7+9HW1ua2bEj7rMScnBzevPs4QRBw8eJF2/Ca+fPnO/1hjyiKqKqqwrZt25Ceno6PP/4YMpnMqdckIv/EziKRD+vt7UVQUBBiYmJgMBhwzz33YNOmTVi2bJm7l+Y3Ghsb8ec//xm/+MUvIJVKJ/RnRFFEf3+/bZiO9ayRXq9HRkYG8vPzUVhYaIv14DbWqxubDanT6WCxWJySDWkwGGzbD5mV6PvstxjHx8dDLpe75Guxo6MDpaWl6OrqwnPPPYc5c+b4/UMkIrph3IZK5I+qq6vx6KOPwmKxQBAEPPDAA9i+fbu7l0XXyWKxQKPR2Abq1NbWQqPRIDg4eFysh6fnM7qTKIowGAzjQtCvNxvSfqKtUqlEfHw833sfNzQ0hKamJoSEhCArK8sluYVarRZ79uzBiRMnsGPHDixfvpzb1YloqrBYJCLyRaIoQqfT4dy5cw7ZkP39/UhNTbVtYbWOzA8KCmIhcxWTzYa0D1j394m2/mJkZAQqlQqjo6MuG15jNptx+PBh7N+/H4899hjWr1/PIUlENNVYLBIR+RNrnp99F7KxsRESiQQzZ860nYcsLCxEcnIyOxTXYB2oY/9rdHQUFosFMTExSE1NRVRUlM9mQ9L/htf09fVBoVC4ZHiNKIo4efIkdu3ahSVLlqCkpASxsbFOvSYR+S0Wi0RE/k4URRiNRodYj5qaGnR1dSE+Pt5hG2tubi7CwsJY/NixZiW2tLQgKSkJiYmJMBgMDtmQ06ZNg1Qq9YlsSPr2oUtHRwfa29sxY8YMpKamuuTBSl1dHbZu3YqoqCiUl5dDqVQ6/ZpE5NdYLBIR0ZWJomjLfjx79ixqampQX18Po9Foi/WwbmfNyMjwuy7kZLISx2ZDarVamM1mr8qGpP/9navVaiQkJLhseE13dzfKysrQ2NiI8vJyLFy4kA9siMgVWCwSEdHkmM1mnD9/3qELeeHCBURERNiKR2shGRUV5ZM3tVORlWjNhrR2IHU6HfR6PSQSicNAHU/IhqT/Da8JDQ2FUql0yfAag8GAl19+GR9++CE2b96MBx980O0PE9577z2Ulpaivr4e//73v3HLLbe4dT1E5FQsFomI6MaJooiBgYFxsR46nQ7p6em2c5B5eXnIysry2lgP+6zErKwsp2Ql2mdDWruQo6OjDtmQkZGRkEqlXvs+ehNr9InRaER2djYiIyOdfk1BEHDkyBHs3bsXq1atwoYNG1xSnE5EfX09AgICsG7dOjz//PMsFol821WLRf70ISKiCZNIJIiNjcXixYuxePFi2+uCIKC5udm2lfWjjz6CWq1GUFAQcnNzHbIhXTEc5HpZC4bR0VEolUqnZiUGBAQgMjJyXFFizYbUarXo6OiATqeDIAgIDQ11OAs5FdmQ9O373dLSgsuXL7ss+kQURXz11VfYvn07Zs+ejc8//xxJSUlOveZk5ebmunsJROQB2FkkIiKnEEURer3eIdajtrYWfX19mD59usNW1lmzZiE4ONhtxY81K3FwcBAKhcLjshLHZkNqtVoYDIbrzoYk9w2vUalU2LFjB8xmMyorK5GXl+f0a96IJUuWsLNI5Pu4DZWIyBUsFgtuueUWpKWl4ejRo+5ejkcSBAGdnZ04e/asbaBOQ0MDACA7O9s2kbWwsBApKSlOvYH39qxEazak/XlIazakfRfSmg1J3xbevb290Gg0SExMREZGhku2+V6+fBm7d+/G6dOn8cwzz+Duu+92++fa3Xffja6urnGvl5WVYcWKFQBYLBL5CRaLRESusGfPHpw5cwZDQ0MsFifBGutRX1/v0IXs7OxEbGyswzCdvLy8G96Cac2h7OjogEwmQ1pamtsHikylK2VDiqKI8PBwhy6kv2VDDg4OoqmpCWFhYS4bXmM0GnHgwAEcOnQIGzZswOrVq72qcGexSOQXeGaRiMjZ2tvbcezYMZSUlGDPnj3uXo5XkUgkCAkJwezZszF79mzb69YIA+tZyLfeegt1dXUYHR2FQqGwFZAFBQXIyMj4zptwURTR2dmJ1tZWJCcnY/78+V514z5RISEhCAkJQXx8vO01QRBsW1mHhoZw8eJFGAwGBAYG+nw2pMFggEqlgslkwqxZs1w2vObo0aOorKzE8uXLcerUKacMSiIiciZ2FomIpsjKlSuxZcsWaLVaPP/88+wsOpHZbEZTU5NDF7K1tRXh4eG2s5DWIjI6OhqiKOLIkSM4cOAAXnrpJSiVSp7t+3++nA05dnhNQkKC068piiKqqqqwdetWZGRkoKysDDKZzOnXnWofffQRnnjiCfT29iImJgazZ8/Gp59+6u5lEZFzcBsqEZEzHT16FJ988gleeeUVfPnllywW3UAURQwNDTnEelRXV6OrqwsWiwUymQwrV67EokWLkJWV5XPds6nk7dmQ9tuM09PTkZqa6pI1tre3o7S0FN3d3XjuuecwZ84cj3tviIiugMUiEZEzbdmyBYcPH0ZgYCBGRkYwNDSEH/3oR3jnnXfcvTS/VVNTg5KSEkybNg3r1q3DyMgIzp49i9raWqhUKgQGBiInJ8fWgSwoKEBiYiJv7q/B07Mhxw6vkcvlLtlmrNVqsWfPHpw4cQI7duzA8uXLva4LS0R+jcUiEZGrsLPoXkNDQ3jiiSfQ3t6OsrIy3HbbbeN+jyiKGB4eRl1dnW0ra01NDXp7e5GSkmLbxlpYWIhZs2Z5ZPfMk5hMJocupDUbMiwszKEL6cxsSOvwmvDwcCiVSoSEhDjlOvbMZjMOHz6M/fv34/HHH8f69evZsSYib8QBN0REANDW1oZFixbhv//9L+Li4tDf34+ioiJ8+eWXyMjIcPfyaApIpVKsXr0aS5YsuWphYt1OOW/ePMybN8/2uiAI6OrqssV67Nu3Dw0NDRAEAVlZWbaBOoWFhS7L5fMGQUFBiIuLQ1xcnO21sdmQXV1d47IhrUN1buT8qMFgQFNTEywWC3JyclwyREYURZw8eRK7du3CkiVL8Le//Q2xsbFOvy4Rkauxs0hEfmf37t1QqVR47bXXsG7dOsjlcmzZssXdyyIPZjQa0dDQ4NCF7OjoQExMjMNE1lK9U64AAAnQSURBVLy8PEilUnYhr2GqsiFNJhOam5vR39+PrKwsh8mvzlRXV4etW7ciKioK5eXlUCqVLrkuEZETcRsqEZGVyWTC3LlzsWbNGrz++uuoqqriZEyaNFEU0dfXZ4v1qK2txblz52AwGJCZmWkrHgsKCpCZmemTER1TyT4bUqvVQq/XXzEbMjg4GB0dHejo6EBGRgamT5/ukuK8u7sbZWVlaGhoQEVFBRYuXMiHAkTkK1gsEhHZ+/TTT3Hvvffis88+w9KlS929HPIhFosFKpXKoQvZ3NyMsLAwh0iPgoICxMTEsOC4Bms2pLUL2dfXB51Oh+DgYMTHx7skG9JgMODll1/Ghx9+iM2bN+PBBx/k9mMi8jUsFomI7G3YsAFHjhzB008/jSeffNLdyyEfJ4oitFqtQ6xHTU0NhoaGkJaWZutCFhYWIjs7m0NSxhgYGEBTUxMiIiKgUCgwbdo0p2dDCoKAI0eOYO/evXj44YdRXFyM0NDQKf7IiIg8AotFIiKrb775Bg8//DD+8pe/4I477sDp06cxffp0dy+L/JAgCLhw4YJtK2t1dTVUKhWmTZuGWbNm2TqQBQUFSEpK8rsu5PDwMFQqFSwWC7Kzs685vGaqsiFFUcRXX32F7du3Y86cOSgtLUVSUpKzPkQiIk/AYpGICPj2RnDBggXYtWsXli5dipdeegn/+te/8Pvf/97dSyMC8L8potZYD2sXsre3F4mJicjPz7d1IXNychAaGupzRaTJZIJGo8Hg4CCysrIcpqxO1rWyIY8ePYro6GjMmTMHRUVF6OnpwY4dO2A2m1FZWYm8vLwp/KiIiDwWi0UiIgB47bXXcPLkSfzxj38E8O35svnz52PPnj1YvHixm1dHdHWiKKKrq8vWhaypqUF9fT3MZrMt1qOgoACFhYVIS0vzynN1giCgra0NFy9edPrwGpPJhC+//BL/+c9/UF1djfr6evT09KCwsBB33XUXbrrpJtx00022ba9ERD6MxSIREZEvMplMtlgPaxeyvb0dUVFRDhNZ8/PzERER4ZFdSFEU0dPTg+bmZiQnJyM9Pd0lBZrRaMTrr7+Ot99+Gxs2bMAjjzyCCxcu2N7H6upqqNVqhISEYP78+XjxxRedviYiIjdgsUhEROQvRFFEf3+/QxeytrYWw8PDkMvlDhNZ3d05sx9eo1QqXRJjIwgCjh49ioqKCvzwhz/Exo0br3ke0mAwoLW1FTk5OU5fGxGRG7BYJCIi3ySXyxEZGYlp06YhMDAQZ86ccfeSPJbFYoFarXaYyqrRaBAaGoq8vDzbWcj8/HzExcU5tQs5PDyMpqYmiKKI7OxsSKVSp13LShRFVFVVYevWrZDL5SgrK0NaWprTr0tE5OFYLBIRkW+Sy+U4c+YMEhIS3L0UrySKInQ6HWprax2yIQcGBpCammrbwmqN9bjRzp/RaERzc/OUDK+ZjPb2dpSWlqKnpwe7d+/GnDlzPHJLLhGRG7BYJCIi38Ri0Tmsw2asXcjq6mo0NTUhICAAM2fOtG1lLSwsRFJS0ncO1LHGhHR2dkIulyMlJcUlxZpWq8Xvfvc7fP755ygtLcWyZcu8cvgPEZETsVgkIiLflJmZidjYWEgkEqxbtw6PP/64u5fks0RRxMjICOrr6x26kN3d3UhISHA4C5mbm4vQ0FCIoog333wTR48exQsvvOCy4TVmsxlvv/029u/fj3Xr1mH9+vUICgpy+nWJiLzQVYvFQFeugoiIaKr985//RGpqKnp6erB06VLk5ORg0aJF7l6WT5JIJAgLC0NRURGKiopsr4uiiO7ublsH8rXXXkN9fT36+/thNpuhUCiwatUqBAQEOL2bKIoiTp48iV27dmHJkiX4+9//jtjYWKdek4jIV7GzSEREPqO0tBQRERF46qmn3L0Uv9bU1ITNmzfDbDZj7dq10Gq1ti5kW1sbIiIibGchrf+MjIy84UKyrq4OJSUliImJwbPPPgulUjlFHxERkU/jNlQiIvI9er0egiAgMjISer0eS5cuxfbt23Hvvfe6e2l+Sa/X4ze/+Q3OnDmD8vLyK3Z4RVHEwMCAbRtrbW0tamtrodPpkJGR4TCRValUIjDwuzdBdXd3o6ysDI2NjaioqMCCBQs4vIaIaOJYLBIRke/RaDS4//77AXx7Rm3VqlUoKSlx86r8l9lsxscff4wVK1ZMeoiMxWJBc3OzQzakWq1GcHAw8vLybBNZ8/PzER8fD4lEguHhYbz88sv46KOPsGXLFjzwwAMcXkNENHksFomIiMi7iKIIvV5vi/WoqalBTU0NLl++jPDwcPT09GD9+vUoLi5GaGioW9f69NNP4+OPP0ZwcDCUSiXeeustxMTEuHVNREQTxGKRiIiIfIMgCDh37hwkEgkKCgrcvRwAwGeffYbvfe97CAwMxKZNmwAAlZWVbl4VEdGEXLVY5F4NIiIi8ioBAQEoLCz0mEIRAO655x7b+crbbrsN7e3tbl4REdGNY7FIRERENIXefPNN3Hfffe5eBhHRDWPOIhEREdEE3H333ejq6hr3ellZGVasWGH798DAQDz88MOuXh4R0ZTjmUUiIiKiKXDo0CHs378fJ0+eRHh4uLuXQ0Q0UVc9s8jOIhEREdENOn78OCorK/HXv/6VhSIR+Qx2FomIiIhuUFZWFkZHRxEfHw/g2yE3+/fvd/OqiIgmhNEZRERERERENA6jM4iIiGhqDQwMYOXKlcjJyUFubi5OnTrl7iUREdEU4plFIiIiui7FxcW499578f7778NoNGJ4eNjdSyIioinEbahEREQ0aUNDQ7j55puh0WggkVx1BxMREXk+bkMlIiKiqaPRaJCYmIif/exnmDNnDtauXQu9Xu/uZRER0RRisUhERESTZjab8fXXX+PnP/85qqqqIJVKUVFR4e5lERHRFGKxSERERJMmk8kgk8lw6623AgBWrlyJr7/+2s2rIiKiqcRikYiIiCYtJSUFM2bMQGNjIwDg5MmTyMvLc/OqiIhoKnHADREREV2Xb775BmvXroXRaIRCocBbb72F2NhYdy+LiIgm56oDblgsEhERERER+S9OQyUiIiIiIqKJY7FIRERERERE47BYJCIiIiIionFYLBIREREREdE4LBaJiIiIiIhoHBaLRERERERENA6LRSIiIiIiIhqHxSIRERERERGNw2KRiIiIiIiIxmGxSEREREREROOwWCQiIiIiIqJxWCwSERERERHROCwWiYiIiIiIaJzA7/j/EpesgoiIiIiIiDwKO4tEREREREQ0DotFIiIiIiIiGofFIhEREREREY3DYpGIiIiIiIjGYbFIRERERERE47BYJCIiIiIionH+Dyyg5qTjWSNoAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(16,9))\n", "ax = fig.add_subplot(111, projection='3d')\n", "ax.plot(xt,yt,zt, label='Kalman Filter Estimate')\n", "ax.plot(Xr, Yr, Zr, label='Real')\n", "ax.set_xlabel('X')\n", "ax.set_ylabel('Y')\n", "ax.set_zlabel('Z')\n", "ax.legend()\n", "plt.title('Ball Trajectory estimated with Kalman Filter')\n", "\n", "# Axis equal\n", "max_range = np.array([Xm.max()-Xm.min(), Ym.max()-Ym.min(), Zm.max()-Zm.min()]).max() / 3.0\n", "mean_x = Xm.mean()\n", "mean_y = Ym.mean()\n", "mean_z = Zm.mean()\n", "ax.set_xlim(mean_x - max_range, mean_x + max_range)\n", "ax.set_ylim(mean_y - max_range, mean_y + max_range)\n", "ax.set_zlim(mean_z - max_range, mean_z + max_range)\n", "plt.savefig('Kalman-Filter-CA-Ball-Trajectory.png', dpi=150, bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Conclusion" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Estimated Position is 0.20m away from ball position.\n" ] } ], "source": [ "dist = np.sqrt((Xm-xt)**2 + (Ym-yt)**2 + (Zm-zt)**2)\n", "print('Estimated Position is %.2fm away from ball position.' % dist[-1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Kalman Filter is just for linear dynamic systems. The drag resistance coefficient is nonlinear with a state, but the filter can handle this until a certain amount of drag.\n", "\n", "But at this time the ball is hitting the ground, the nonlinearity is too much and the filter is providing a wrong solution. Therefore, one have to model a switch in the filter loop, which helps the filter to get it." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fragen? [@Balzer82](https://twitter.com/balzer82)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.7" } }, "nbformat": 4, "nbformat_minor": 1 }